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Popular >

derivative of x^2cos^4(x)

Solution

derivative of

x^{2} cos^{4} (x)

Solution

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

Solution steps

\frac{d}{d x} (x^{2} cos^{4} (x))

Apply the Product Rule:

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

f = x^{2}, g = cos^{4} (x)

= \frac{d}{d x} (x^{2}) cos^{4} (x) + \frac{d}{d x} (cos^{4} (x)) x^{2}

\frac{d}{d x} (x^{2}) = 2 x

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

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

Simplify

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

Popular Examples

integral from 1 to 3 of (4z-z^2)

\int_{1}^{3} (4 z - z^{2}) d z

y^{^{'}} + 4 y = 2 x

integral of (x^2)/((169+x^2)^2)

\int \frac{x ^{2}}{( 169 + x ^{2} ) ^{2}} d x

sum from n=0 to infinity of nz^n

n = 0 \sum \infty n z^{n}

integral of ((2x+1))/((x+1)(x-2)(x-3))

\int \frac{( 2 x + 1 )}{( x + 1 ) ( x - 2 ) ( x - 3 )} d x

Frequently Asked Questions (FAQ)

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