What is the derivative of 3cos^3(5x) ?

The derivative of 3cos^3(5x) is -45cos^2(5x)sin(5x)

What is the first derivative of 3cos^3(5x) ?

The first derivative of 3cos^3(5x) is -45cos^2(5x)sin(5x)

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derivative of

3 cos^{3} (5 x)

- 45 cos^{2} (5 x) sin (5 x)

Solution steps

\frac{d}{d x} (3 cos^{3} (5 x))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 3 \frac{d}{d x} (cos^{3} (5 x))

Apply the chain rule:

3 (cos (5 x))^{2} \frac{d}{d x} (cos (5 x))

= 3 (cos (5 x))^{2} \frac{d}{d x} (cos (5 x))

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= 3 \cdot 3 (cos (5 x))^{2} (- sin (5 x) \cdot 5)

Simplify

= - 45 cos^{2} (5 x) sin (5 x)

What is the derivative of 3cos^3(5x) ?
The derivative of 3cos^3(5x) is -45cos^2(5x)sin(5x)
What is the first derivative of 3cos^3(5x) ?
The first derivative of 3cos^3(5x) is -45cos^2(5x)sin(5x)