Chain Rule

Chain Rule

Poll

The Chain Rule is feeling like...

• A hot, sunny fantastic day

• A slightly drizzly day, but warm

• Cold sleet whipping me across the face

Multiple Choice

Identify if the following would require the Chain Rule:
 $\frac{d}{dx}\left[h\left(t\left(x\right)\right)\right]$  

• Yes

• No

Multiple Choice

Identify if the following would require the Chain Rule:
 $\frac{d}{dx}\left[f\left(x\right)\cdot g\left(x\right)\right]$  

• Yes

• No

Multiple Choice

What is the "outer" part of the composite function:
 $\sqrt{x^2+1}$  

•  $\sqrt{x}$  

•  $x^2+1$  

• This is not a composite function

Multiple Choice

What is the "inner" part of the composite function:
 $\left(\sin x\right)^2$  

•  $x^2$  

•  $\sin x$  

• This is not a composite function

Multiple Choice

What is the "outer" part for this composite function:
 $2\left(x^3-1\right)^2$  

•  $2x^2$  

•  $x^3-1$  

• This is not a composite function.

Multiple Choice

What is f'(x) if f(x) = cos(5x⁴)?

• f'(x) = sin(20x³)
• f'(x) = 20x³ sin(5x⁴)
• f'(x) = -sin(20x³)
• f'(x) = -20x³ sin(5x⁴)

Multiple Choice

Find y' if y = tan(3x²+2).

• sec²(3x²+2)
• 6xsec²(3x²+2)
• 6xsec²x(3x²+2)
• sec²(6x)

Multiple Choice

Multiple Choice

Multiple Choice

Differentiate:
f(x) = x⁷ (5 + 8x)³

• f '(x) = x² (5 + 8x)⁶ (35 + 80x)
• f '(x) = x⁶ (5 + 8x)² (35 + 80x)
• f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)
• f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

Multiple Choice

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)

Multiple Choice

find y' for y= (2x+1)¹⁰

• 10(2x+1)⁹

• 20(2x-1)⁹

• 20(2x+1)¹⁰

• 20(2x+1)⁹

Multiple Choice

find y' for y=(e^5x)+1

• 5e^5x+1

• e^5x

• 5e^5x

• 1

Multiple Choice

• A

• B

• C

• D

• E

Multiple Choice

• A

• B

• C

• D

Multiple Choice

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

• f '(x) = 5x⁵(x⁴ + 4)⁴

• f '(x) = 6x⁵(x⁶ + 4)⁴

• f '(x) = 30x⁵(x⁶ + 4)⁴

• f '(x) = 30x⁶(x⁶ + 4)⁴

Multiple Choice

CHALLENGE:
Find the derivative of following with respect to x:
 $f\left(x\right)=\sqrt{\cos\left(x\right)}$  

• f '(x) =  $-\frac{\sin\left(x\right)}{2\cos^2\left(x\right)}$  

• f '(x) =  $\frac{2\sin\left(x\right)}{\sqrt{\cos\left(x\right)}}$  

• f '(x) =  $-\frac{\sin\left(x\right)}{2\sqrt{\cos\left(x\right)}}$  

• f '(x) =  $-\frac{\sin\left(x\right)}{\sqrt{\cos\left(x\right)}}$