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Popular >

derivative of e^{ax}+ae^{ax}x

Solution

\frac{d}{d x} (e^{a x} + a e^{a x} x)

Solution

a^{2} e^{a x} x + 2 a e^{a x}

Solution steps

\frac{d}{d x} (e^{a x} + a e^{a x} x)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (e^{a x}) + \frac{d}{d x} (a e^{a x} x)

\frac{d}{d x} (e^{a x}) = e^{a x} a

\frac{d}{d x} (a e^{a x} x) = a (a e^{a x} x + e^{a x})

= e^{a x} a + a (a e^{a x} x + e^{a x})

Simplify

e^{a x} a + a (a e^{a x} x + e^{a x}) : a^{2} e^{a x} x + 2 a e^{a x}

= a^{2} e^{a x} x + 2 a e^{a x}

Graph

Popular Examples

derivative of 9sin(x)

\frac{d}{d x} (9 sin (x))

derivative of 2x^{-1}

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

integral from 4 to 6 of y/(y^2-3)

\int_{4}^{6} \frac{y}{y ^{2} - 3} d y

derivative of (x^3/(48)+4/x)

\frac{d}{d x} (\frac{x ^{3}}{48} + \frac{4}{x})

integral of 1/(sin(x)tan(x))

\int \frac{1}{sin ( x ) tan ( x )} d x

Frequently Asked Questions (FAQ)

What is the derivative of e^{ax}+ae^{ax}x ?
The derivative of e^{ax}+ae^{ax}x is a^2e^{ax}x+2ae^{ax}
What is the first derivative of e^{ax}+ae^{ax}x ?
The first derivative of e^{ax}+ae^{ax}x is a^2e^{ax}x+2ae^{ax}