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Popular >

derivative of ax^2e^{5x}

Solution

\frac{d}{d x} (a x^{2} e^{5 x})

Solution

a (2 x e^{5 x} + e^{5 x} \cdot 5 x^{2})

Solution steps

\frac{d}{d x} (a x^{2} e^{5 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= a \frac{d}{d x} (x^{2} e^{5 x})

Apply the Product Rule:

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

f = x^{2}, g = e^{5 x}

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (e^{5 x}) = e^{5 x} \cdot 5

= a (2 x e^{5 x} + e^{5 x} \cdot 5 x^{2})

Popular Examples

laplacetransform t^4+3e^{3t}t^2+e^{-t}t+1 laplace transform

t^{4} + 3 e^{3 t} t^{2} + e^{- t} t + 1

tangent of-(4x)/(x^2+1)tangent of

- \frac{4 x}{x ^{2} + 1}

limit as x approaches infinity of x+8

x \to \infty lim (x + 8)

derivative of 8x^3e^{-x}

\frac{d}{d x} (8 x^{3} e^{- x})

derivative of xe^{kx}

\frac{d}{d x} (x e^{k x})

Frequently Asked Questions (FAQ)

What is the derivative of ax^2e^{5x} ?
The derivative of ax^2e^{5x} is a(2xe^{5x}+e^{5x}*5x^2)
What is the first derivative of ax^2e^{5x} ?
The first derivative of ax^2e^{5x} is a(2xe^{5x}+e^{5x}*5x^2)