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

The derivative of (x^2(x+1^2)/(sqrt(x-1))) is (7x^4+2x^3-9x^2-4x)/(2(x-1)sqrt(x-1))

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

The first derivative of (x^2(x+1^2)/(sqrt(x-1))) is (7x^4+2x^3-9x^2-4x)/(2(x-1)sqrt(x-1))

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

\frac{7 x ^{4} + 2 x ^{3} - 9 x ^{2} - 4 x}{2 ( x - 1 ) x - 1}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x^{2} (x + 1)^{2}) = 4 x^{3} + 6 x^{2} + 2 x

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

= \frac{( 4 x ^{3} + 6 x ^{2} + 2 x ) x - 1 - \frac{1}{2 x - 1} x ^{2} ( x + 1 ) ^{2}}{( x - 1 ) ^{2}}

Simplify

\frac{( 4 x ^{3} + 6 x ^{2} + 2 x ) x - 1 - \frac{1}{2 x - 1} x ^{2} ( x + 1 ) ^{2}}{( x - 1 ) ^{2}} : \frac{7 x ^{4} + 2 x ^{3} - 9 x ^{2} - 4 x}{2 ( x - 1 ) x - 1}

= \frac{7 x ^{4} + 2 x ^{3} - 9 x ^{2} - 4 x}{2 ( x - 1 ) x - 1}

6 4 x^{2} + 5

\frac{d}{d x} (e^{y - l n (x)})

\frac{d}{d x} (\frac{x ^{4}}{x ^{5} + 3})

\frac{\partial}{\partial y} (3 x + y)

\int \frac{23}{23 + e ^{x}} d x

What is the derivative of (x^2(x+1^2)/(sqrt(x-1))) ?
The derivative of (x^2(x+1^2)/(sqrt(x-1))) is (7x^4+2x^3-9x^2-4x)/(2(x-1)sqrt(x-1))
What is the first derivative of (x^2(x+1^2)/(sqrt(x-1))) ?
The first derivative of (x^2(x+1^2)/(sqrt(x-1))) is (7x^4+2x^3-9x^2-4x)/(2(x-1)sqrt(x-1))