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Popular Calculus >

derivative of f(x)=x^5cos(2x)

Solution

derivative of

f (x) = x^{5} cos (2 x)

Solution

5 x^{4} cos (2 x) - 2 x^{5} sin (2 x)

Solution steps

\frac{d}{d x} (x^{5} cos (2 x))

Apply the Product Rule:

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

f = x^{5}, g = cos (2 x)

= \frac{d}{d x} (x^{5}) cos (2 x) + \frac{d}{d x} (cos (2 x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= 5 x^{4} cos (2 x) + (- sin (2 x) \cdot 2) x^{5}

Simplify

= 5 x^{4} cos (2 x) - 2 x^{5} sin (2 x)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^5cos(2x) ?
The derivative of f(x)=x^5cos(2x) is 5x^4cos(2x)-2x^5sin(2x)
What is the first derivative of f(x)=x^5cos(2x) ?
The first derivative of f(x)=x^5cos(2x) is 5x^4cos(2x)-2x^5sin(2x)