What is the derivative of (3x/((x^2+1)^{3/5)}) ?

The derivative of (3x/((x^2+1)^{3/5)}) is (3(-x^2+5))/(5(x^2+1)^{8/5)}

What is the first derivative of (3x/((x^2+1)^{3/5)}) ?

The first derivative of (3x/((x^2+1)^{3/5)}) is (3(-x^2+5))/(5(x^2+1)^{8/5)}

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\frac{d}{d x} (\frac{3 x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

\frac{3 ( - x ^{2} + 5 )}{5 ( x ^{2} + 1 ) ^{\frac{8}{5}}}

Solution steps

\frac{d}{d x} (\frac{3 x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{x}{( x ^{2} + 1 ) ^{\frac{3}{5}}})

Apply the Quotient Rule:

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

= 3 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 1 ) ^{\frac{3}{5}} - \frac{d}{d x} ( ( x ^{2} + 1 ) ^{\frac{3}{5}} ) x}{( ( x ^{2} + 1 ) ^{\frac{3}{5}} ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} ((x^{2} + 1)^{\frac{3}{5}}) = \frac{6 x}{5 ( x ^{2} + 1 ) ^{\frac{2}{5}}}

= 3 \cdot \frac{1 \cdot ( x ^{2} + 1 ) ^{\frac{3}{5}} - \frac{6 x}{5 ( x ^{2} + 1 ) ^{\frac{2}{5}}} x}{( ( x ^{2} + 1 ) ^{\frac{3}{5}} ) ^{2}}

Simplify

3 \cdot \frac{1 \cdot ( x ^{2} + 1 ) ^{\frac{3}{5}} - \frac{6 x}{5 ( x ^{2} + 1 ) ^{\frac{2}{5}}} x}{( ( x ^{2} + 1 ) ^{\frac{3}{5}} ) ^{2}} : \frac{3 ( - x ^{2} + 5 )}{5 ( x ^{2} + 1 ) ^{\frac{8}{5}}}

= \frac{3 ( - x ^{2} + 5 )}{5 ( x ^{2} + 1 ) ^{\frac{8}{5}}}

(x^{2} - 2 x + 4), 2

\int \frac{1}{x ^{2} 4 x ^{2} - 1} d x

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

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

\int e^{x} x cos (x) d x

What is the derivative of (3x/((x^2+1)^{3/5)}) ?
The derivative of (3x/((x^2+1)^{3/5)}) is (3(-x^2+5))/(5(x^2+1)^{8/5)}
What is the first derivative of (3x/((x^2+1)^{3/5)}) ?
The first derivative of (3x/((x^2+1)^{3/5)}) is (3(-x^2+5))/(5(x^2+1)^{8/5)}