Chain Rule Lesson Slides: 9 Slides

9 Slides • 8 Questions

1

Chain Rule on Differentiation

2

Multiple Choice

Which one is the same as

\left(f\ \circ\ g\right)\left(x\right)

1

$g\left(f\left(x\right)\right)$

2

$f\left(g\left(x\right)\right)$

3

Multiple Choice

Given $f\left(x\right)=2x$ and
$g(x)=x^2+3$ , find $\left(f\ \circ\ g\right)\left(x\right)$ .

1

$x^2+2x+3$

2

$4x^2+3$

3

$2x^2+3$

4

$2x^2+6$

4

Multiple Choice

Given $f\left(x\right)=3x+10$
and $g\left(x\right)=x-2\$ .
Find $\left(f\ \circ\ g\right)\left(5\right)$

1

19

2

23

3

-10

4

None of these.

5

6

7

8

9

10

11

12

13

Multiple Choice

find $y'$ for $y=\left(2x+1\right)^{10}$

1

10(2x+1)⁹

2

20(2x-1)⁹

3

20(2x+1)¹⁰

4

20(2x+1)⁹

14

Multiple Choice

Find the derivative of f(x) = (x⁶ + 4)⁵

1

f '(x) = 5x⁵(x⁴ + 4)⁴

2

f '(x) = 6x⁵(x⁶ + 4)⁴

3

f '(x) = 30x⁵(x⁶ + 4)⁴

4

f '(x) = 30x⁶(x⁶ + 4)⁴

15

Multiple Choice

Find the derivative
f(t) = (t² + 2t)⁵

1

f'(t) = 5(2t+2)⁴

2

f'(t) = 5(t² + 2t)⁴

3

f'(t) = 5(t² + 2t)⁴(2t)

4

f'(t) = 5(t² + 2t)⁴(2t + 2)

16

Multiple Choice

Given $F\left(x\right)=\left(\frac{x}{2x+1}\right)^3$ , find $F'\left(x\right)$ .

1

$3\left(\frac{x}{2x+1}\right)^2$

2

$3\left[\frac{1}{\left(2x+1\right)^2}\right]^2$

3

$\frac{1}{2}$

4

$\frac{3x^2}{\left(2x+1\right)^4}$

17

Multiple Choice

Differentiate $f\left(x\right)=\sqrt{x^2-1}$ .

1

$f'\left(x\right)=\sqrt{x^2-1}$

2

$f'\left(x\right)=\frac{1}{2x\sqrt{x^2-1}}$

3

$f'\left(x\right)=\frac{x}{\sqrt{x^2-1}}$

4

$f'\left(x\right)=x\sqrt{x^2-1}$

Chain Rule on Differentiation

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