What is the derivative of-(15/(8x^{7/2)}) ?

The derivative of-(15/(8x^{7/2)}) is (105)/(16x^{9/2)}

What is the first derivative of-(15/(8x^{7/2)}) ?

The first derivative of-(15/(8x^{7/2)}) is (105)/(16x^{9/2)}

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\frac{d}{d x} (- \frac{15}{8 x ^{\frac{7}{2}}})

\frac{105}{16 x ^{\frac{9}{2}}}

Solution steps

\frac{d}{d x} (- \frac{15}{8 x ^{\frac{7}{2}}})

Take the constant out:

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

= - \frac{15}{8} \frac{d}{d x} (\frac{1}{x ^{\frac{7}{2}}})

Apply exponent rule:

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

= - \frac{15}{8} \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}{8} (- \frac{7}{2} x^{- \frac{7}{2} - 1})

Simplify

- \frac{15}{8} (- \frac{7}{2} x^{- \frac{7}{2} - 1}) : \frac{105}{16 x ^{\frac{9}{2}}}

= \frac{105}{16 x ^{\frac{9}{2}}}

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 2 e^{3 t}

\int \frac{- 2 sec ^{2} ( x )}{( 4 + tan ( x ) ) ^{3}} d x

y = e^{9 e^{x}}

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

What is the derivative of-(15/(8x^{7/2)}) ?
The derivative of-(15/(8x^{7/2)}) is (105)/(16x^{9/2)}
What is the first derivative of-(15/(8x^{7/2)}) ?
The first derivative of-(15/(8x^{7/2)}) is (105)/(16x^{9/2)}