What is the derivative of-(15/(16x^{7/2)}) ?

The derivative of-(15/(16x^{7/2)}) is (105)/(32x^{9/2)}

What is the first derivative of-(15/(16x^{7/2)}) ?

The first derivative of-(15/(16x^{7/2)}) is (105)/(32x^{9/2)}

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\frac{d}{d x} (- \frac{15}{16 x ^{\frac{7}{2}}})

\frac{105}{32 x ^{\frac{9}{2}}}

Solution steps

\frac{d}{d x} (- \frac{15}{16 x ^{\frac{7}{2}}})

Take the constant out:

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

= - \frac{15}{16} \frac{d}{d x} (\frac{1}{x ^{\frac{7}{2}}})

Apply exponent rule:

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

= - \frac{15}{16} \frac{d}{d x} (x^{- \frac{7}{2}})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= - \frac{15}{16} (- \frac{7}{2} x^{- \frac{7}{2} - 1})

Simplify

- \frac{15}{16} (- \frac{7}{2} x^{- \frac{7}{2} - 1}) : \frac{105}{32 x ^{\frac{9}{2}}}

= \frac{105}{32 x ^{\frac{9}{2}}}

x \to 0 lim (\frac{sin ^{3} ( x )}{x})

\frac{3 x}{x ^{2} + 3}

y^{^{'}} = \frac{x}{3 y}

\int \frac{6}{1 - cos ( 3 x )} d x

\int_{0}^{1} x x^{2} + 8 d x

What is the derivative of-(15/(16x^{7/2)}) ?
The derivative of-(15/(16x^{7/2)}) is (105)/(32x^{9/2)}
What is the first derivative of-(15/(16x^{7/2)}) ?
The first derivative of-(15/(16x^{7/2)}) is (105)/(32x^{9/2)}