What is the derivative of (x^2/(x^2+2x-15)) ?

The derivative of (x^2/(x^2+2x-15)) is (2x^2-30x)/((x^2+2x-15)^2)

What is the first derivative of (x^2/(x^2+2x-15)) ?

The first derivative of (x^2/(x^2+2x-15)) is (2x^2-30x)/((x^2+2x-15)^2)

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\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 2 x - 15})

\frac{2 x ^{2} - 30 x}{( x ^{2} + 2 x - 15 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 2 x - 15})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} ) ( x ^{2} + 2 x - 15 ) - \frac{d}{d x} ( x ^{2} + 2 x - 15 ) x ^{2}}{( x ^{2} + 2 x - 15 ) ^{2}}

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

\frac{d}{d x} (x^{2} + 2 x - 15) = 2 x + 2

= \frac{2 x ( x ^{2} + 2 x - 15 ) - ( 2 x + 2 ) x ^{2}}{( x ^{2} + 2 x - 15 ) ^{2}}

Expand

2 x (x^{2} + 2 x - 15) - (2 x + 2) x^{2} : 2 x^{2} - 30 x

= \frac{2 x ^{2} - 30 x}{( x ^{2} + 2 x - 15 ) ^{2}}

\int 5 x sin^{2} (x) d x

\frac{\partial}{\partial x} (sin (2 x) cos (2 y))

\frac{x ^{2}}{1 - x ^{2}}

\int 15 x^{\frac{1}{2}} d x

\int_{- 2}^{2} x^{2} + 3 x - 4 d x

What is the derivative of (x^2/(x^2+2x-15)) ?
The derivative of (x^2/(x^2+2x-15)) is (2x^2-30x)/((x^2+2x-15)^2)
What is the first derivative of (x^2/(x^2+2x-15)) ?
The first derivative of (x^2/(x^2+2x-15)) is (2x^2-30x)/((x^2+2x-15)^2)