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Popular >

derivative of {r}(xcos(x))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = r (x), g = cos (x)

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

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

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

Simplify

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

Popular Examples

integral of y*cos(xy)

\int y \cdot cos (x y) d x

sum from n=0 to infinity of 1

n = 0 \sum \infty 1

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

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

integral of 1/(sqrt(x)-\sqrt[3]{x)}

\int \frac{1}{x - 3 x} d x

derivative of y=(18)/(x^2+2)derivative of

y = \frac{18}{x ^{2} + 2}

Frequently Asked Questions (FAQ)

What is the derivative of {r}(xcos(x)) ?
The derivative of {r}(xcos(x)) is cos(x) derivative of {r}(x)-sin(x){r}(x)
What is the first derivative of {r}(xcos(x)) ?
The first derivative of {r}(xcos(x)) is cos(x) derivative of {r}(x)-sin(x){r}(x)