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Popular >

derivative of cos^4(x/4)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral of (14x+1)sqrt(7x^2+x)

\int (14 x + 1) 7 x^{2} + x d x

x^2(dy)/(dx)+x(x+2)y=e^x

x^{2} \frac{d y}{d x} + x (x + 2) y = e^{x}

integral of 7/((x-3)(x+4))

\int \frac{7}{( x - 3 ) ( x + 4 )} d x

laplacetransform e^{-t/4}laplace transform

e^{- \frac{t}{4}}

limit as t approaches 1 of e^{4t}

t \to 1 lim (e^{4 t})

Frequently Asked Questions (FAQ)

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