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Popular >

derivative of sqrt(x)cos(x)

Solution

\frac{d}{d x} (x cos (x))

Solution

\frac{cos ( x )}{2 x} - x sin (x)

Solution steps

\frac{d}{d x} (x cos (x))

Apply the Product Rule:

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

f = x, g = cos (x)

= \frac{d}{d x} (x) cos (x) + \frac{d}{d x} (cos (x)) x

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

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

= \frac{1}{2 x} cos (x) + (- sin (x)) x

Simplify

\frac{1}{2 x} cos (x) + (- sin (x)) x : \frac{cos ( x )}{2 x} - x sin (x)

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

Popular Examples

integral of cos^7(x)tan^3(x)

\int cos^{7} (x) tan^{3} (x) d x

derivative of x^{sqrt(5)}

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

integral of (8x)/(sqrt(1-x^4))

\int \frac{8 x}{1 - x ^{4}} d x

integral of (cos^7(x))sin(x)

\int (cos^{7} (x)) sin (x) d x

derivative of cos^2(x-sin^2(x))

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

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)cos(x) ?
The derivative of sqrt(x)cos(x) is (cos(x))/(2sqrt(x))-sqrt(x)sin(x)
What is the first derivative of sqrt(x)cos(x) ?
The first derivative of sqrt(x)cos(x) is (cos(x))/(2sqrt(x))-sqrt(x)sin(x)