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Popular >

derivative of xsin(x+xcos(x))

Solution

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

Solution

sin (x) + x cos (x) + cos (x) - x sin (x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= sin (x) + x cos (x) + cos (x) - x sin (x)

Popular Examples

sum from n=0 to infinity of (7/4)^n

n = 0 \sum \infty (\frac{7}{4})^{n}

limit as x approaches infinity+of 1/(5x)

x \to \infty + lim (\frac{1}{5 x})

tangent of f(x)=sqrt(3x+40),\at x=3 tangent of

f (x) = 3 x + 40, at x = 3

integral of ((3e^{-x}+2e^{3x})/(e^{2x)})

\int (\frac{3 e ^{- x} + 2 e ^{3 x}}{e ^{2 x}}) d x

y^'=(t(t^2+1))/(4y^3)

y^{^{'}} = \frac{t ( t ^{2} + 1 )}{4 y ^{3}}

Frequently Asked Questions (FAQ)

What is the derivative of xsin(x+xcos(x)) ?
The derivative of xsin(x+xcos(x)) is sin(x)+xcos(x)+cos(x)-xsin(x)
What is the first derivative of xsin(x+xcos(x)) ?
The first derivative of xsin(x+xcos(x)) is sin(x)+xcos(x)+cos(x)-xsin(x)