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Popular Calculus >

derivative of acos(x+x^2sin(x))

Solution

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

Solution

- a sin (x) + 2 x sin (x) + cos (x) x^{2}

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Graph

Popular Examples

limit as x approaches 0 of (sin(3/5)x)/x

x \to 0 lim (\frac{sin ( \frac{3}{5} ) x}{x})

integral of cos^4(5x)

\int cos^{4} (5 x) d x

derivative of sin(2x+10)

\frac{d}{d x} (sin (2 x) + 10)

derivative of 5/(x^2)

d er i v a t i v e \frac{5}{x ^{2}}

integral from 0 to 1.75 of 1250x

\int_{0}^{1.75} 1250 x d x

Frequently Asked Questions (FAQ)

What is the derivative of acos(x+x^2sin(x)) ?
The derivative of acos(x+x^2sin(x)) is -asin(x)+2xsin(x)+cos(x)x^2
What is the first derivative of acos(x+x^2sin(x)) ?
The first derivative of acos(x+x^2sin(x)) is -asin(x)+2xsin(x)+cos(x)x^2