What is the derivative of f(x)=x^2cos^4(x) ?

The derivative of f(x)=x^2cos^4(x) is 2xcos^4(x)-4x^2cos^3(x)sin(x)

What is the first derivative of f(x)=x^2cos^4(x) ?

The first derivative of f(x)=x^2cos^4(x) is 2xcos^4(x)-4x^2cos^3(x)sin(x)

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derivative of

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

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)

\int 4 t^{3} d t

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

\frac{d}{d x} (x^{4} + 8 x^{2} - x)

\int_{2}^{3} (3 x^{2} + 2 x + 3) d x

y^{^{''}} + 11 y^{^{'}} + 24 y = 0

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