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

The derivative of f(x)=(x^2)/(3+8x) is (6x+8x^2)/((3+8x)^2)

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

The first derivative of f(x)=(x^2)/(3+8x) is (6x+8x^2)/((3+8x)^2)

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derivative of

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

\frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d}{d x} (3 + 8 x) = 8

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

Expand

2 x (3 + 8 x) - 8 x^{2} : 6 x + 8 x^{2}

= \frac{6 x + 8 x ^{2}}{( 3 + 8 x ) ^{2}}

(\frac{x ^{2}}{2})^{^{'}}

\int_{0}^{4} x 17 - x^{2} d x

\int_{0}^{1} \frac{x ^{4} + 6}{x} d x

tan^{4} (2 x - 1)^{3}

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

What is the derivative of f(x)=(x^2)/(3+8x) ?
The derivative of f(x)=(x^2)/(3+8x) is (6x+8x^2)/((3+8x)^2)
What is the first derivative of f(x)=(x^2)/(3+8x) ?
The first derivative of f(x)=(x^2)/(3+8x) is (6x+8x^2)/((3+8x)^2)