What is the derivative of (x^3+x^2e^{2x}) ?

The derivative of (x^3+x^2e^{2x}) is 2e^{2x}x^3+5e^{2x}x^2+2e^{2x}x

What is the first derivative of (x^3+x^2e^{2x}) ?

The first derivative of (x^3+x^2e^{2x}) is 2e^{2x}x^3+5e^{2x}x^2+2e^{2x}x

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\frac{d}{d x} ((x^{3} + x^{2}) e^{2 x})

2 e^{2 x} x^{3} + 5 e^{2 x} x^{2} + 2 e^{2 x} x

Solution steps

\frac{d}{d x} ((x^{3} + x^{2}) e^{2 x})

Apply the Product Rule:

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

f = x^{3} + x^{2}, g = e^{2 x}

= \frac{d}{d x} (x^{3} + x^{2}) e^{2 x} + \frac{d}{d x} (e^{2 x}) (x^{3} + x^{2})

\frac{d}{d x} (x^{3} + x^{2}) = 3 x^{2} + 2 x

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

= (3 x^{2} + 2 x) e^{2 x} + e^{2 x} \cdot 2 (x^{3} + x^{2})

Simplify

(3 x^{2} + 2 x) e^{2 x} + e^{2 x} \cdot 2 (x^{3} + x^{2}) : 2 e^{2 x} x^{3} + 5 e^{2 x} x^{2} + 2 e^{2 x} x

= 2 e^{2 x} x^{3} + 5 e^{2 x} x^{2} + 2 e^{2 x} x

\int x 2 - \frac{1}{2 x} d x

x \to 0 lim (\frac{x + 6}{x ^{2} + 3})

\int x^{4} sec^{2} (x^{5} + 2) d x

y^{^{'}} + 3 y = 2 sin (e^{3 x})

\int x^{3} sin^{2} (1 + x^{\frac{5}{2}}) d x

What is the derivative of (x^3+x^2e^{2x}) ?
The derivative of (x^3+x^2e^{2x}) is 2e^{2x}x^3+5e^{2x}x^2+2e^{2x}x
What is the first derivative of (x^3+x^2e^{2x}) ?
The first derivative of (x^3+x^2e^{2x}) is 2e^{2x}x^3+5e^{2x}x^2+2e^{2x}x