What is the derivative of y = ln ⁡ ( x 2 x + 1 ) y=\ln\left(\frac{x}{2x+1}\right) y = ln ( 2 x + 1 x )

d y d x = 1 x − 2 2 x + 1 \frac{dy}{dx}=\frac{1}{x}-\frac{2}{2x+1} d x d y = x 1 − 2 x + 1 2

d y d x = 1 x − 1 2 x + 1 \frac{dy}{dx}=\frac{1}{x}-\frac{1}{2x+1} d x d y = x 1 − 2 x + 1 1

d y d x = 1 x + 2 2 x + 1 \frac{dy}{dx}=\frac{1}{x}+\frac{2}{2x+1} d x d y = x 1 + 2 x + 1 2

d y d x = 1 x + 1 2 x + 1 \frac{dy}{dx}=\frac{1}{x}+\frac{1}{2x+1} d x d y = x 1 + 2 x + 1 1

What is the derivative of y = ln ⁡ ( x e x ) y=\ln\left(xe^x\right) y = ln ( x e x )

d y d x = 1 x + 1 \frac{dy}{dx}=\frac{1}{x}+1 d x d y = x 1 + 1

d y d x = 1 x + e x \frac{dy}{dx}=\frac{1}{x}+e^x d x d y = x 1 + e x

d y d x = 1 x e x \frac{dy}{dx}=\frac{1}{xe^x} d x d y = x e x 1

d y d x = 1 x − 1 \frac{dy}{dx}=\frac{1}{x}-1 d x d y = x 1 − 1

What is the derivative of y = ln ⁡ ( 5 x e x ) y=\ln\left(\frac{5x}{e^x}\right) y = ln ( e x 5 x )

d y d x = 1 x − 1 \frac{dy}{dx}=\frac{1}{x}-1 d x d y = x 1 − 1

d y d x = 1 x + 1 \frac{dy}{dx}=\frac{1}{x}+1 d x d y = x 1 + 1

d y d x = 1 x − e x \frac{dy}{dx}=\frac{1}{x}-e^x d x d y = x 1 − e x

d y d x = 1 x + e x \frac{dy}{dx}=\frac{1}{x}+e^x d x d y = x 1 + e x

Differentiate logarithms

Authored by HALIMATUL BM

Mathematics

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MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of
$y=\ln2x$

$\frac{dy}{dx}=\frac{1}{2x}$

$\frac{dy}{dx}=\frac{1}{x}$

$\frac{dy}{dx}=\frac{2}{x}$

$\frac{dy}{dx}=\frac{1}{x^2}$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of
$y=2\ln\left(x^2+3x\right)$

$\frac{dy}{dx}=\frac{2x}{x^2+3x}$

$\frac{dy}{dx}=\frac{2}{x^2+3x}$

$\frac{dy}{dx}=\frac{2x+3}{x^2+3x}$

$\frac{dy}{dx}=\frac{4x+6}{x^2+3x}$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of
$y=\ln\left(\frac{x}{2x+1}\right)$

$\frac{dy}{dx}=\frac{1}{x}-\frac{2}{2x+1}$

$\frac{dy}{dx}=\frac{1}{x}-\frac{1}{2x+1}$

$\frac{dy}{dx}=\frac{1}{x}+\frac{2}{2x+1}$

$\frac{dy}{dx}=\frac{1}{x}+\frac{1}{2x+1}$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of
$y=\ln\left(xe^x\right)$

$\frac{dy}{dx}=\frac{1}{x}+e^x$

$\frac{dy}{dx}=\frac{1}{x}+1$

$\frac{dy}{dx}=\frac{1}{xe^x}$

$\frac{dy}{dx}=\frac{1}{x}-1$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of
$y=\ln\left(x^2e^{x^2}\right)$

$\frac{dy}{dx}=\frac{1}{2x}+e^{x^2}$

$\frac{dy}{dx}=\frac{1}{2x}+2x$

$\frac{dy}{dx}=\frac{2}{x}+2x$

$\frac{dy}{dx}=\frac{1}{x^2}+2x$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of
$y=\ln\left(x^2+3\right)^5$

$\frac{dy}{dx}=\frac{10x}{x^2+3}$

$\frac{dy}{dx}=\frac{5x}{x^2+3}$

$\frac{dy}{dx}=\frac{2x}{x^2+3}$

$\frac{dy}{dx}=\frac{10}{x^2+3}$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of
$y=\ln x^6$

$\frac{dy}{dx}=\frac{1}{6x}$

$\frac{dy}{dx}=\frac{6}{x}$

$\frac{dy}{dx}=\frac{1}{6x}$

$\frac{dy}{dx}=\frac{1}{x^6}$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of
$y=\ln\left(\frac{5x}{e^x}\right)$

$\frac{dy}{dx}=\frac{1}{x}-1$

$\frac{dy}{dx}=\frac{1}{x}+1$

$\frac{dy}{dx}=\frac{1}{x}-e^x$

$\frac{dy}{dx}=\frac{1}{x}+e^x$

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of
$y=\ln\left(\frac{x^2+3}{x^3}\right)$

$\frac{dy}{dx}=\frac{x}{x^2+3}-\frac{3}{x}$

$\frac{dy}{dx}=\frac{2x}{x^2+3}-\frac{3}{x}$

$\frac{dy}{dx}=\frac{1}{x^2+3}-\frac{1}{x^3}$

$\frac{dy}{dx}=\frac{x}{x^2+3}-\frac{1}{x^3}$

10.

MULTIPLE CHOICE QUESTION

3 mins • 1 pt

What is the derivative of
$y=\ln\left(x\left(x^3+4\right)^5\right)$

$\frac{dy}{dx}=\frac{1}{x}+\frac{15x^2}{x^3+4}$

$\frac{dy}{dx}=\frac{1}{x}+\frac{3x^2}{x^3+4}$

$\frac{dy}{dx}=\frac{5}{x}+\frac{3x^2}{x^3+4}$

$\frac{dy}{dx}=\frac{5}{x}+\frac{5}{x^3+4}$

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Differentiate logarithms

What is the derivative of y=ln⁡2xy=\ln2xy=ln2x

What is the derivative of y=2ln⁡(x2+3x)y=2\ln\left(x^2+3x\right)y=2ln(x2+3x)

What is the derivative of y=ln⁡(x2x+1)y=\ln\left(\frac{x}{2x+1}\right)y=ln(2x+1x​)

What is the derivative of y=ln⁡(xex)y=\ln\left(xe^x\right)y=ln(xex)

What is the derivative of y=ln⁡(x2ex2)y=\ln\left(x^2e^{x^2}\right)y=ln(x2ex2)

What is the derivative of y=ln⁡(x2+3)5y=\ln\left(x^2+3\right)^5y=ln(x2+3)5

What is the derivative of y=ln⁡x6y=\ln x^6y=lnx6

What is the derivative of y=ln⁡(5xex)y=\ln\left(\frac{5x}{e^x}\right)y=ln(ex5x​)

What is the derivative of y=ln⁡(x2+3x3)y=\ln\left(\frac{x^2+3}{x^3}\right)y=ln(x3x2+3​)

What is the derivative of y=ln⁡(x(x3+4)5)y=\ln\left(x\left(x^3+4\right)^5\right)y=ln(x(x3+4)5)

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What is the derivative of
$y=\ln2x$

What is the derivative of
$y=2\ln\left(x^2+3x\right)$

What is the derivative of
$y=\ln\left(\frac{x}{2x+1}\right)$

What is the derivative of
$y=\ln\left(xe^x\right)$

What is the derivative of
$y=\ln\left(x^2e^{x^2}\right)$

What is the derivative of
$y=\ln\left(x^2+3\right)^5$

What is the derivative of
$y=\ln x^6$

What is the derivative of
$y=\ln\left(\frac{5x}{e^x}\right)$

What is the derivative of
$y=\ln\left(\frac{x^2+3}{x^3}\right)$

What is the derivative of
$y=\ln\left(x\left(x^3+4\right)^5\right)$