What is the derivative of (2x+1)/((x^2+1)^{1.5)} ?

The derivative of (2x+1)/((x^2+1)^{1.5)} is (2(x^2+1)^{1.5}-3x(2x+1)sqrt(x^2+1))/((x^2+1)^3)

What is the first derivative of (2x+1)/((x^2+1)^{1.5)} ?

The first derivative of (2x+1)/((x^2+1)^{1.5)} is (2(x^2+1)^{1.5}-3x(2x+1)sqrt(x^2+1))/((x^2+1)^3)

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derivative of

\frac{2 x + 1}{( x ^{2} + 1 ) ^{1.5}}

\frac{2 ( x ^{2} + 1 ) ^{1.5} - 3 x ( 2 x + 1 ) x ^{2} + 1}{( x ^{2} + 1 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{2 x + 1}{( x ^{2} + 1 ) ^{1.5}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x + 1 ) ( x ^{2} + 1 ) ^{1.5} - \frac{d}{d x} ( ( x ^{2} + 1 ) ^{1.5} ) ( 2 x + 1 )}{( ( x ^{2} + 1 ) ^{1.5} ) ^{2}}

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

\frac{d}{d x} ((x^{2} + 1)^{1.5}) = 3 x x^{2} + 1

= \frac{2 ( x ^{2} + 1 ) ^{1.5} - 3 x x ^{2} + 1 ( 2 x + 1 )}{( ( x ^{2} + 1 ) ^{1.5} ) ^{2}}

((x^{2} + 1)^{1.5})^{2} = (x^{2} + 1)^{3}

= \frac{2 ( x ^{2} + 1 ) ^{1.5} - 3 x ( 2 x + 1 ) x ^{2} + 1}{( x ^{2} + 1 ) ^{3}}

What is the derivative of (2x+1)/((x^2+1)^{1.5)} ?
The derivative of (2x+1)/((x^2+1)^{1.5)} is (2(x^2+1)^{1.5}-3x(2x+1)sqrt(x^2+1))/((x^2+1)^3)
What is the first derivative of (2x+1)/((x^2+1)^{1.5)} ?
The first derivative of (2x+1)/((x^2+1)^{1.5)} is (2(x^2+1)^{1.5}-3x(2x+1)sqrt(x^2+1))/((x^2+1)^3)