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Popular >

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

Solution

derivative of

f (x) = 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

integral of 1/(x(x^2+x+5))

\int \frac{1}{x ( x ^{2} + x + 5 )} d x

(\partial)/(\partial x)((6-x^2y^2)^2)

\frac{\partial}{\partial x} ((6 - x^{2} y^{2})^{2})

limit as x approaches 4+of (4+x)/(4-x)

x \to 4 + lim (\frac{4 + x}{4 - x})

limit as h approaches 0 of 6x+1+3h

h \to 0 lim (6 x + 1 + 3 h)

inverse oflaplace {1/(s^2+s-20)}inverse laplace

{\frac{1}{s ^{2} + s - 20}}

Frequently Asked Questions (FAQ)

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