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Popular >

derivative of x*cos^3(4x)

Solution

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

Solution

cos^{3} (4 x) - 12 x cos^{2} (4 x) sin (4 x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = cos^{3} (4 x)

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

\frac{d x}{d x} = 1

\frac{d}{d x} (cos^{3} (4 x)) = - 12 cos^{2} (4 x) sin (4 x)

= 1 \cdot cos^{3} (4 x) + (- 12 cos^{2} (4 x) sin (4 x)) x

Simplify

= cos^{3} (4 x) - 12 x cos^{2} (4 x) sin (4 x)

Popular Examples

derivative of x^4+e^{-x}

\frac{d}{d x} (x^{4} + e^{- x})

limit as x approaches 0 of 2x+4

x \to 0 lim (2 x + 4)

limit as x approaches 0 of 9x-6

x \to 0 lim (9 x - 6)

integral of-cos(x)+sin(x)+C

\int - cos (x) + sin (x) + C d x

(d^3x)/(dt^3)-3x=0

\frac{d ^{3} x}{d t ^{3}} - 3 x = 0

Frequently Asked Questions (FAQ)

What is the derivative of x*cos^3(4x) ?
The derivative of x*cos^3(4x) is cos^3(4x)-12xcos^2(4x)sin(4x)
What is the first derivative of x*cos^3(4x) ?
The first derivative of x*cos^3(4x) is cos^3(4x)-12xcos^2(4x)sin(4x)