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Popular >

(sqrt(x)cos(sqrt(x)))^'

Solution

(x cos (x))^{^{'}}

Solution

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

Solution steps

(x cos (x))^{'}

Apply the Product Rule:

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

f = x, g = cos (x)

= (x)^{^{'}} cos (x) + (cos (x))^{^{'}} x

(x)^{'} = \frac{1}{2 x}

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

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

Simplify

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

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

Graph

Popular Examples

integral of cos(x)sec^2(x)

\int cos (x) sec^{2} (x) d x

f (x) = - sec^{2} (x)

integral from 0 to pi/4 of 4sec^3(x)

\int_{0}^{\frac{π}{4}} 4 sec^{3} (x) d x

limit as x approaches 4 of 1/((x-4)^2)

x \to 4 lim (\frac{1}{( x - 4 ) ^{2}})

integral of 10-1/16 x

\int 10 - \frac{1}{16} x d x

Frequently Asked Questions (FAQ)

What is the (sqrt(x)cos(sqrt(x)))^' ?
The (sqrt(x)cos(sqrt(x)))^' is (cos(sqrt(x))}{2sqrt(x)}-\frac{sin(sqrt(x)))/2
What is the first (sqrt(x)cos(sqrt(x)))^' ?
The first (sqrt(x)cos(sqrt(x)))^' is (cos(sqrt(x))}{2sqrt(x)}-\frac{sin(sqrt(x)))/2