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Popular >

derivative of (x+5cos(x))

Solution

\frac{d}{d x} ((x + 5) cos (x))

Solution

cos (x) - sin (x) (x + 5)

Solution steps

\frac{d}{d x} ((x + 5) cos (x))

Apply the Product Rule:

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

f = x + 5, g = cos (x)

= \frac{d}{d x} (x + 5) cos (x) + \frac{d}{d x} (cos (x)) (x + 5)

\frac{d}{d x} (x + 5) = 1

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

= 1 \cdot cos (x) + (- sin (x)) (x + 5)

Simplify

= cos (x) - sin (x) (x + 5)

Graph

Popular Examples

integral from 0 to 3 of (1/2 x-1)

\int_{0}^{3} (\frac{1}{2} x - 1) d x

y ln (y) d x + x d y = 0

tangent of y=x^3-3x^2-9x+27,\at x=4 tangent of

y = x^{3} - 3 x^{2} - 9 x + 27, at x = 4

integral from-1 to 0 of (x^2-3)

\int_{- 1}^{0} (x^{2} - 3) d x

integral of (2x+1)/((x^2+x+1)^2)

\int \frac{2 x + 1}{( x ^{2} + x + 1 ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x+5cos(x)) ?
The derivative of (x+5cos(x)) is cos(x)-sin(x)(x+5)
What is the first derivative of (x+5cos(x)) ?
The first derivative of (x+5cos(x)) is cos(x)-sin(x)(x+5)