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Popular >

derivative of ae^{2x}+bxe^{2x}

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Graph

Popular Examples

(\partial)/(\partial x)(x/(x^2+y^2)+3x)

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + y ^{2}} + 3 x)

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

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

limit as x approaches 5 of (6+1/x)^2

x \to 5 lim ((6 + \frac{1}{x})^{2})

integral of (21)/(xln(8x))

\int \frac{21}{x ln ( 8 x )} d x

area y^2-5x=1,x-y=1 area

y^{2} - 5 x = 1, x - y = 1

Frequently Asked Questions (FAQ)

What is the derivative of ae^{2x}+bxe^{2x} ?
The derivative of ae^{2x}+bxe^{2x} is ae^{2x}*2+b(e^{2x}+2e^{2x}x)
What is the first derivative of ae^{2x}+bxe^{2x} ?
The first derivative of ae^{2x}+bxe^{2x} is ae^{2x}*2+b(e^{2x}+2e^{2x}x)