What is the derivative of cos^4(θ+5) ?

The derivative of cos^4(θ+5) is -4cos^3(θ+5)sin(θ+5)

What is the first derivative of cos^4(θ+5) ?

The first derivative of cos^4(θ+5) is -4cos^3(θ+5)sin(θ+5)

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derivative of

cos^{4} (θ + 5)

- 4 cos^{3} (θ + 5) sin (θ + 5)

Solution steps

\frac{d}{d θ} (cos^{4} (θ + 5))

Apply the chain rule:

4 (cos (θ + 5))^{3} \frac{d}{d θ} (cos (θ + 5))

= 4 (cos (θ + 5))^{3} \frac{d}{d θ} (cos (θ + 5))

\frac{d}{d θ} (cos (θ + 5)) = - sin (θ + 5)

= 4 (cos (θ + 5))^{3} (- sin (θ + 5))

Simplify

= - 4 cos^{3} (θ + 5) sin (θ + 5)

What is the derivative of cos^4(θ+5) ?
The derivative of cos^4(θ+5) is -4cos^3(θ+5)sin(θ+5)
What is the first derivative of cos^4(θ+5) ?
The first derivative of cos^4(θ+5) is -4cos^3(θ+5)sin(θ+5)