What is the derivative of f(x)=(3x^2e^x-4)/(x^2) ?

The derivative of f(x)=(3x^2e^x-4)/(x^2) is (3e^xx^3+8)/(x^3)

What is the first derivative of f(x)=(3x^2e^x-4)/(x^2) ?

The first derivative of f(x)=(3x^2e^x-4)/(x^2) is (3e^xx^3+8)/(x^3)

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derivative of

f (x) = \frac{3 x ^{2} e ^{x} - 4}{x ^{2}}

\frac{3 e ^{x} x ^{3} + 8}{x ^{3}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{3 ( e ^{x} x ^{2} + 2 e ^{x} x ) x ^{2} - 2 x ( 3 x ^{2} e ^{x} - 4 )}{( x ^{2} ) ^{2}} : \frac{3 e ^{x} x ^{3} + 8}{x ^{3}}

= \frac{3 e ^{x} x ^{3} + 8}{x ^{3}}

What is the derivative of f(x)=(3x^2e^x-4)/(x^2) ?
The derivative of f(x)=(3x^2e^x-4)/(x^2) is (3e^xx^3+8)/(x^3)
What is the first derivative of f(x)=(3x^2e^x-4)/(x^2) ?
The first derivative of f(x)=(3x^2e^x-4)/(x^2) is (3e^xx^3+8)/(x^3)