Differentiation

slope of the tangent line

slope of the normal line

exponent

potato

Sign

Maximum/Minimum

Instantaneous rate of change

Common Denominator

The function is increasing

The function is decreasing

3x²

x³

6x

3x² + x³

0

2

-2

None of the above

(n-1)xⁿ

nxⁿ⁺¹

(n+1)x^n-1

nx^n-1

6x² + 6x

6x + 2

6x + 6

6x² + 6

6x² + 6x

6x + 2

6x + 6

6x² + 6

at C only

at points A, C and E only

at point B and D only

at points A and E only

product rule

quotient rule

power rule

sum rule

1/(x - 1)^-1

-1/(x - 1)^-2

-1/(x - 1)

-1/(x - 1)²

y'=10xe^3x(2x+3)

y'=5xe^3x(3x+2)

y'=10ex^3x(3x+2)

y'=5xe^3x(2x+3)

 $4e^{\left(4x+2\right)}$  

 $\frac{4}{e^{\left(4x+2\right)}}$  

 $e^{\left(4x+2\right)}\left(8x^2+2x\right)$  

 $\frac{\left(8x^2+2x\right)}{e^{\left(4x+2\right)}}$  

 $3\left(e^x+2\right)\left(e^x+2x\right)^2$  

 $3\left(e^x+2\right)^2$  

 $3\left(e^x+4x^2\right)\left(e^x+2x\right)^2$  

 $4\left(e^x+2\right)^4$  

sinx

-sinx

-cscx cotx

sec²x

 $\cos x$  

 $-\cos x$  

 $\sin^{-1}x$  

 $\frac{1}{\sin x}$  

 $\sin x\cos x$  

 $\sec x\tan x$  

 $-\sec x\tan x$  

 $\sec^{-1}x$  

 $\frac{1}{\sec x}$  

 $\csc x\cot x$  

 $-\csc x\cot x$  

 $\csc x\cot x$  

 $\csc^{-1}x\cot^{-1}x$  

 $\frac{1}{\csc x\cot x}$  

 $-\sec x\tan x$  

cscx cotx

secx tanx

sec²x

-cscx cotx

 $-\csc^2x$  

 $\csc^2x$  

 $\cot^{-1}x$  

 $\frac{1}{\cot x}$  

 $\csc x$  

2cos(x)

2sin(2x)

2cos(2x)

2xcos(2x)

 $12\tan^3x\sec^2x$  

 $12\tan^3x\sec x$  

 $12\sec^3x$  

 $12\sec^6x$  

 $12\sec^2x$  

 $\frac{x\cos x-2\sin x}{x^3}$  

 $-\frac{x\cos x+2\sin x}{x^3}$  

 $\frac{x\cos x+2\sin x}{x^3}$  

 $\frac{-x\cos x+2\sin x}{x^3}$  

 $\frac{x\cos x-2\sin x}{x^4}$  

 $-4\sin\left(2x\right)+8\cos\left(2x+3\right)$  

 $4\sin\left(2x\right)+8\cos\left(2x+3\right)$  

 $-4\sin\left(2x\right)-8\cos\left(2x+3\right)$  

 $4\sin\left(2x\right)-8\cos\left(2x+3\right)$  

 $-4\sin\left(2x\right)\cos\left(2x\right)+8\sin\left(2x+3\right)\cos\left(2x+3\right)$  

 $\frac{3\cos x-4\sin x}{2\sqrt{3\sin x+4\cos x}}$  

 $\frac{3\cos x+4\sin x}{2\sqrt{3\sin x+4\cos x}}$  

 $\frac{3}{2}\left(3\cos x-4\sin x\right)\sqrt{\left(3\sin x+4\cos x\right)^3}$  

 $\frac{3}{2}\left(3\cos x+4\sin x\right)\sqrt{\left(3\sin x+4\cos x\right)^3}$  

 $-\frac{3\cos x-4\sin x}{2\sqrt{3\sin x+4\cos x}}$  

 $\frac{2x\left(\cos x+x\sin x\right)}{\cos^3x}$  

 $\frac{2x\left(\cos x-x\sin x\right)}{\cos^3x}$  

 $\frac{2x\left(\cos^2x+x\sin x\right)}{\cos^4x}$  

 $\frac{2x\left(\cos^2x-x\sin x\right)}{\cos^4x}$  

 $-\frac{2x\left(\cos x+x\sin x\right)}{\cos^3x}$  

 $2\cos x+3x^2$  

 $-2\cos x+3x^2$  

 $2\cos x+4x^4$  

 $2\cos x+2x^2$  

 $-2\cos x+2x^2$  

 $\frac{2}{2x+1}-\frac{2}{1-2x}$  

 $\frac{2}{2x+1}+\frac{2}{1-2x}$  

 $\frac{2}{2x-1}+\frac{2}{1-2x}$  

 $\frac{2}{2x+1}+\frac{2}{1+2x}$  

 $x^x\left(1+\ln x\right)$  

 $x^x\left(\ln x\right)$  

 $x.x^{x-1}$  

 $\left(1+\ln x\right)$