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Popular >

derivative of y=2x^2e^x+4x^3

Solution

derivative of

y = 2 x^{2} e^{x} + 4 x^{3}

Solution

2 (2 x e^{x} + e^{x} x^{2}) + 12 x^{2}

Solution steps

\frac{d}{d x} (2 x^{2} e^{x} + 4 x^{3})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (2 x^{2} e^{x}) + \frac{d}{d x} (4 x^{3})

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

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

= 2 (2 x e^{x} + e^{x} x^{2}) + 12 x^{2}

Popular Examples

limit as x approaches 0 of (1-5x)^{7/x}

x \to 0 lim ((1 - 5 x)^{\frac{7}{x}})

derivative of (sqrt(x))/(x+13)derivative of

\frac{x}{x + 13}

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

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

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

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

derivative of sqrt(6/5)*cos(x)

\frac{d}{d x} (\frac{6}{5} \cdot cos (x))

Frequently Asked Questions (FAQ)

What is the derivative of y=2x^2e^x+4x^3 ?
The derivative of y=2x^2e^x+4x^3 is 2(2xe^x+e^xx^2)+12x^2
What is the first derivative of y=2x^2e^x+4x^3 ?
The first derivative of y=2x^2e^x+4x^3 is 2(2xe^x+e^xx^2)+12x^2