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

The derivative of y=(3x^2+2)/(sqrt(x+1)) is (9x^2+12x-2)/(2(x+1)sqrt(x+1))

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

The first derivative of y=(3x^2+2)/(sqrt(x+1)) is (9x^2+12x-2)/(2(x+1)sqrt(x+1))

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derivative of

y = \frac{3 x ^{2} + 2}{x + 1}

\frac{9 x ^{2} + 12 x - 2}{2 ( x + 1 ) x + 1}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{6 x x + 1 - \frac{1}{2 x + 1} ( 3 x ^{2} + 2 )}{( x + 1 ) ^{2}} : \frac{9 x ^{2} + 12 x - 2}{2 ( x + 1 ) x + 1}

= \frac{9 x ^{2} + 12 x - 2}{2 ( x + 1 ) x + 1}

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

\frac{d ^{3}}{d x ^{3}} (4 x - 3)

\int \frac{2 x + 6}{x ^{2} + 1} d x

x \to 2 - lim (3 - x)

\frac{d}{d x} (csc (4 x^{4} - 2))

What is the derivative of y=(3x^2+2)/(sqrt(x+1)) ?
The derivative of y=(3x^2+2)/(sqrt(x+1)) is (9x^2+12x-2)/(2(x+1)sqrt(x+1))
What is the first derivative of y=(3x^2+2)/(sqrt(x+1)) ?
The first derivative of y=(3x^2+2)/(sqrt(x+1)) is (9x^2+12x-2)/(2(x+1)sqrt(x+1))