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Popular >

derivative of (x^2+xcos(5x))

Solution

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

Solution

cos (5 x) (2 x + 1) - 5 sin (5 x) (x^{2} + x)

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{2} + x) = 2 x + 1

\frac{d}{d x} (cos (5 x)) = - sin (5 x) \cdot 5

= (2 x + 1) cos (5 x) + (- sin (5 x) \cdot 5) (x^{2} + x)

Simplify

= cos (5 x) (2 x + 1) - 5 sin (5 x) (x^{2} + x)

Graph

Popular Examples

integral of (1/x+1)/(x^2)

\int \frac{\frac{1}{x} + 1}{x ^{2}} d x

tangent of f(x)=4\sqrt[3]{x},\at x=1 tangent of

f (x) = 4 3 x, at x = 1

integral from 3 to 3 of (x+1)

\int_{3}^{3} (x + 1) d x

derivative of 7/(\sqrt[5]{x)}derivative of

\frac{7}{5 x}

derivative of x^2-5x+1/(x^{3/2})

\frac{d}{d x} (x^{2} - 5 x + \frac{1}{x ^{\frac{3}{2}}})

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+xcos(5x)) ?
The derivative of (x^2+xcos(5x)) is cos(5x)(2x+1)-5sin(5x)(x^2+x)
What is the first derivative of (x^2+xcos(5x)) ?
The first derivative of (x^2+xcos(5x)) is cos(5x)(2x+1)-5sin(5x)(x^2+x)