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Popular >

derivative of f(x)=x^5cos(2x)

Solution

derivative of

f (x) = x^{5} cos (2 x)

Solution

5 x^{4} cos (2 x) - 2 x^{5} sin (2 x)

Solution steps

\frac{d}{d x} (x^{5} cos (2 x))

Apply the Product Rule:

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

f = x^{5}, g = cos (2 x)

= \frac{d}{d x} (x^{5}) cos (2 x) + \frac{d}{d x} (cos (2 x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (cos (2 x)) = - sin (2 x) \cdot 2

= 5 x^{4} cos (2 x) + (- sin (2 x) \cdot 2) x^{5}

Simplify

= 5 x^{4} cos (2 x) - 2 x^{5} sin (2 x)

Popular Examples

integral from-2 to 3 of (x^3-6x)

\int_{- 2}^{3} (x^{3} - 6 x) d x

integral of x/(x^2sin^2(ln(x)))

\int \frac{x}{x ^{2} sin ^{2} ( ln ( x ) )} d x

tangent of ((x+5))/((x-5))tangent of

\frac{( x + 5 )}{( x - 5 )}

tangent of f(x)=x^2-tan(x),\at x=0 tangent of

f (x) = x^{2} - tan (x), at x = 0

(\partial)/(\partial y)(9e^{yz}cos(xyz))

\frac{\partial}{\partial y} (9 e^{yz} cos (x yz))

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^5cos(2x) ?
The derivative of f(x)=x^5cos(2x) is 5x^4cos(2x)-2x^5sin(2x)
What is the first derivative of f(x)=x^5cos(2x) ?
The first derivative of f(x)=x^5cos(2x) is 5x^4cos(2x)-2x^5sin(2x)