What is the derivative of (3x^2/(sqrt(x^2+2x-1))) ?

The derivative of (3x^2/(sqrt(x^2+2x-1))) is (3(x^3+3x^2-2x))/((x^2+2x-1)sqrt(x^2+2x-1))

What is the first derivative of (3x^2/(sqrt(x^2+2x-1))) ?

The first derivative of (3x^2/(sqrt(x^2+2x-1))) is (3(x^3+3x^2-2x))/((x^2+2x-1)sqrt(x^2+2x-1))

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\frac{d}{d x} (\frac{3 x ^{2}}{x ^{2} + 2 x - 1})

\frac{3 ( x ^{3} + 3 x ^{2} - 2 x )}{( x ^{2} + 2 x - 1 ) x ^{2} + 2 x - 1}

Solution steps

\frac{d}{d x} (\frac{3 x ^{2}}{x ^{2} + 2 x - 1})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{x ^{2}}{x ^{2} + 2 x - 1})

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

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

\frac{d}{d x} (x^{2} + 2 x - 1) = \frac{x + 1}{x ^{2} + 2 x - 1}

= 3 \cdot \frac{2 x x ^{2} + 2 x - 1 - \frac{x + 1}{x ^{2} + 2 x - 1} x ^{2}}{( x ^{2} + 2 x - 1 ) ^{2}}

Simplify

3 \cdot \frac{2 x x ^{2} + 2 x - 1 - \frac{x + 1}{x ^{2} + 2 x - 1} x ^{2}}{( x ^{2} + 2 x - 1 ) ^{2}} : \frac{3 ( x ^{3} + 3 x ^{2} - 2 x )}{( x ^{2} + 2 x - 1 ) x ^{2} + 2 x - 1}

= \frac{3 ( x ^{3} + 3 x ^{2} - 2 x )}{( x ^{2} + 2 x - 1 ) x ^{2} + 2 x - 1}

f (x) = x^{3} - 3 x + 1, at x = 2

\int e^{x} - x e^{x} d x

f (x) = - \frac{42}{( x + 4 ) ^{4}}

\int_{0}^{5} \frac{1}{x ^{\frac{20}{19}}} d x

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

What is the derivative of (3x^2/(sqrt(x^2+2x-1))) ?
The derivative of (3x^2/(sqrt(x^2+2x-1))) is (3(x^3+3x^2-2x))/((x^2+2x-1)sqrt(x^2+2x-1))
What is the first derivative of (3x^2/(sqrt(x^2+2x-1))) ?
The first derivative of (3x^2/(sqrt(x^2+2x-1))) is (3(x^3+3x^2-2x))/((x^2+2x-1)sqrt(x^2+2x-1))