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

The derivative of 4cos^5(x) is -20cos^4(x)sin(x)

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

The first derivative of 4cos^5(x) is -20cos^4(x)sin(x)

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\frac{d}{d x} (4 cos^{5} (x))

- 20 cos^{4} (x) sin (x)

Solution steps

\frac{d}{d x} (4 cos^{5} (x))

Take the constant out:

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

= 4 \frac{d}{d x} (cos^{5} (x))

Apply the chain rule:

5 (cos (x))^{4} \frac{d}{d x} (cos (x))

= 5 (cos (x))^{4} \frac{d}{d x} (cos (x))

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

= 4 \cdot 5 (cos (x))^{4} (- sin (x))

Simplify

= - 20 cos^{4} (x) sin (x)

\frac{\partial}{\partial y} (2 e^{x} cos (yz))

\frac{1}{3} (\frac{d x}{d t}) - 2 e^{- t} = - x

d er i v a t i v e e^{2 x} tan (x)

t a y l or (1 - x)^{- \frac{1}{2}}

\frac{d y}{d t} + y = \frac{1}{1 + e ^{2 t}}

What is the derivative of 4cos^5(x) ?
The derivative of 4cos^5(x) is -20cos^4(x)sin(x)
What is the first derivative of 4cos^5(x) ?
The first derivative of 4cos^5(x) is -20cos^4(x)sin(x)