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Popular >

derivative of (cos(pix-16)^4)

Solution

\frac{d}{d x} ((cos (π x - 16))^{4})

Solution

- 4 π cos^{3} (π x - 16) sin (π x - 16)

Solution steps

\frac{d}{d x} ((cos (π x - 16))^{4})

Apply the chain rule:

4 (cos (π x - 16))^{3} \frac{d}{d x} (cos (π x - 16))

= 4 (cos (π x - 16))^{3} \frac{d}{d x} (cos (π x - 16))

\frac{d}{d x} (cos (π x - 16)) = - sin (π x - 16) π

= 4 (cos (π x - 16))^{3} (- sin (π x - 16) π)

Simplify

= - 4 π cos^{3} (π x - 16) sin (π x - 16)

Popular Examples

integral of 1/(sqrt(-x^2-6x))

\int \frac{1}{- x ^{2} - 6 x} d x

area x=-y,x=2y+3,y=-2,y=1 area

x = - y, x = 2 y + 3, y = - 2, y = 1

derivative of xln(3)

\frac{d}{d x} (x ln (3))

derivative of f(x)=sqrt(x)+1 derivative of

f (x) = x + 1

(dx)/(x(y-1))+(dy)/(y(x+2))=0,y(1)=1

\frac{d x}{x ( y - 1 )} + \frac{d y}{y ( x + 2 )} = 0, y (1) = 1

Frequently Asked Questions (FAQ)

What is the derivative of (cos(pix-16)^4) ?
The derivative of (cos(pix-16)^4) is -4picos^3(pix-16)sin(pix-16)
What is the first derivative of (cos(pix-16)^4) ?
The first derivative of (cos(pix-16)^4) is -4picos^3(pix-16)sin(pix-16)