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Popular >

derivative of x^5cos(x)

Solution

derivative of

x^{5} cos (x)

Solution

5 x^{4} cos (x) - x^{5} sin (x)

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}) = 5 x^{4}

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

= 5 x^{4} cos (x) + (- sin (x)) x^{5}

Simplify

= 5 x^{4} cos (x) - x^{5} sin (x)

Popular Examples

derivative of (x^2-1/(x+3))

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

integral of 1/(25-x^2)

\int \frac{1}{25 - x ^{2}} d x

integral of (2x^2)/(e^x)

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

f^'(x)=0.7sin(x)-1.1cos(x)

f^{^{'}} (x) = 0.7 sin (x) - 1.1 cos (x)

derivative of t/2 derivative of

\frac{t}{2}

Frequently Asked Questions (FAQ)

What is the derivative of x^5cos(x) ?
The derivative of x^5cos(x) is 5x^4cos(x)-x^5sin(x)
What is the first derivative of x^5cos(x) ?
The first derivative of x^5cos(x) is 5x^4cos(x)-x^5sin(x)