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Popular Calculus >

derivative of-(cos^4(x)/4)

Solution

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

Solution

cos^{3} (x) sin (x)

Solution steps

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

Take the constant out:

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

= - \frac{1}{4} \frac{d}{d x} (cos^{4} (x))

Apply the chain rule:

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

= 4 (cos (x))^{3} \frac{d}{d x} (cos (x))

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

= - \frac{1}{4} \cdot 4 (cos (x))^{3} (- sin (x))

Simplify

- \frac{1}{4} \cdot 4 cos^{3} (x) (- sin (x)) : cos^{3} (x) sin (x)

= cos^{3} (x) sin (x)

Graph

Popular Examples

integral of 1-e^{-2x}

\int 1 - e^{- 2 x} d x

sin(x)sec(y)dx=dy

sin (x) sec (y) d x = d y

integral of (-1)/(sqrt(1-x^2))

\int \frac{- 1}{1 - x ^{2}} d x

derivative of (1+x/x)

\frac{d}{d x} (\frac{1 + x}{x})

derivative of (2.4)/(sqrt(5+1x))

d er i v a t i v e \frac{2.4}{5 + 1 x}

Frequently Asked Questions (FAQ)

What is the derivative of-(cos^4(x)/4) ?
The derivative of-(cos^4(x)/4) is cos^3(x)sin(x)
What is the first derivative of-(cos^4(x)/4) ?
The first derivative of-(cos^4(x)/4) is cos^3(x)sin(x)