What is the derivative of f(x)=(3x^2)/(x^3-8) ?

The derivative of f(x)=(3x^2)/(x^3-8) is (3(-x^4-16x))/((x^3-8)^2)

What is the first derivative of f(x)=(3x^2)/(x^3-8) ?

The first derivative of f(x)=(3x^2)/(x^3-8) is (3(-x^4-16x))/((x^3-8)^2)

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derivative of

f (x) = \frac{3 x ^{2}}{x ^{3} - 8}

\frac{3 ( - x ^{4} - 16 x )}{( x ^{3} - 8 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x ^{2}}{x ^{3} - 8})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{x ^{2}}{x ^{3} - 8})

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d}{d x} ( x ^{2} ) ( x ^{3} - 8 ) - \frac{d}{d x} ( x ^{3} - 8 ) x ^{2}}{( x ^{3} - 8 ) ^{2}}

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

\frac{d}{d x} (x^{3} - 8) = 3 x^{2}

= 3 \cdot \frac{2 x ( x ^{3} - 8 ) - 3 x ^{2} x ^{2}}{( x ^{3} - 8 ) ^{2}}

Simplify

3 \cdot \frac{2 x ( x ^{3} - 8 ) - 3 x ^{2} x ^{2}}{( x ^{3} - 8 ) ^{2}} : \frac{3 ( - x ^{4} - 16 x )}{( x ^{3} - 8 ) ^{2}}

= \frac{3 ( - x ^{4} - 16 x )}{( x ^{3} - 8 ) ^{2}}

4 x^{10 x^{3}}

f (x) = ln (3^{2 - x^{2}})

\int \frac{x + 4}{x + 2} d x

\int (5 x^{3} - 3 x^{2} - 4 x + 50) d x

\int 2 x^{2} - 8 d x

What is the derivative of f(x)=(3x^2)/(x^3-8) ?
The derivative of f(x)=(3x^2)/(x^3-8) is (3(-x^4-16x))/((x^3-8)^2)
What is the first derivative of f(x)=(3x^2)/(x^3-8) ?
The first derivative of f(x)=(3x^2)/(x^3-8) is (3(-x^4-16x))/((x^3-8)^2)