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

The derivative of f(x)= 3/((2x+1)^{5/2)} is -(15)/((2x+1)^{7/2)}

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

The first derivative of f(x)= 3/((2x+1)^{5/2)} is -(15)/((2x+1)^{7/2)}

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derivative of

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

- \frac{15}{( 2 x + 1 ) ^{\frac{7}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

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

Apply the chain rule:

- \frac{5}{2 ( 2 x + 1 ) ^{\frac{7}{2}}} \frac{d}{d x} (2 x + 1)

= - \frac{5}{2 ( 2 x + 1 ) ^{\frac{7}{2}}} \frac{d}{d x} (2 x + 1)

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

= 3 (- \frac{5}{2 ( 2 x + 1 ) ^{\frac{7}{2}}} \cdot 2)

Simplify

3 (- \frac{5}{2 ( 2 x + 1 ) ^{\frac{7}{2}}} \cdot 2) : - \frac{15}{( 2 x + 1 ) ^{\frac{7}{2}}}

= - \frac{15}{( 2 x + 1 ) ^{\frac{7}{2}}}

x y^{^{'}} - y = - x^{2} + 2 x + 2

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

\frac{\partial}{\partial y} (8 x ln (x y))

t^{2} \cdot y^{^{'}} + t \cdot y = 5

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

What is the derivative of f(x)= 3/((2x+1)^{5/2)} ?
The derivative of f(x)= 3/((2x+1)^{5/2)} is -(15)/((2x+1)^{7/2)}
What is the first derivative of f(x)= 3/((2x+1)^{5/2)} ?
The first derivative of f(x)= 3/((2x+1)^{5/2)} is -(15)/((2x+1)^{7/2)}