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Popular >

derivative of sin(xsqrt(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = sin (x), g = x

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

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

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

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

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

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

Graph

Popular Examples

tangent of f(x)=7e^x+4x,\at x=0 tangent of

f (x) = 7 e^{x} + 4 x, at x = 0

integral of 5^xe^{-x}

\int 5^{x} e^{- x} d x

(\partial)/(\partial x)((x-a)^{-1})

\frac{\partial}{\partial x} ((x - a)^{- 1})

integral of (x^2)/(sqrt(2x-x^2))

\int \frac{x ^{2}}{2 x - x ^{2}} d x

integral of 4sin(wt)e^t

\int 4 sin (wt) e^{t} d t

Frequently Asked Questions (FAQ)

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