What is the derivative of 3/((3-x^8^{3/2)}) ?

The derivative of 3/((3-x^8^{3/2)}) is (36x^7)/((3-x^8)^{5/2)}

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

The first derivative of 3/((3-x^8^{3/2)}) is (36x^7)/((3-x^8)^{5/2)}

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\frac{d}{d x} (\frac{3}{( 3 - x ^{8} ) ^{\frac{3}{2}}})

\frac{36 x ^{7}}{( 3 - x ^{8} ) ^{\frac{5}{2}}}

Solution steps

\frac{d}{d x} (\frac{3}{( 3 - x ^{8} ) ^{\frac{3}{2}}})

Take the constant out:

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

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

Apply exponent rule:

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

= 3 \frac{d}{d x} ((3 - x^{8})^{- \frac{3}{2}})

Apply the chain rule:

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

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

\frac{d}{d x} (3 - x^{8}) = - 8 x^{7}

= 3 (- \frac{3}{2 ( 3 - x ^{8} ) ^{\frac{5}{2}}} (- 8 x^{7}))

Simplify

3 (- \frac{3}{2 ( 3 - x ^{8} ) ^{\frac{5}{2}}} (- 8 x^{7})) : \frac{36 x ^{7}}{( 3 - x ^{8} ) ^{\frac{5}{2}}}

= \frac{36 x ^{7}}{( 3 - x ^{8} ) ^{\frac{5}{2}}}

What is the derivative of 3/((3-x^8^{3/2)}) ?
The derivative of 3/((3-x^8^{3/2)}) is (36x^7)/((3-x^8)^{5/2)}
What is the first derivative of 3/((3-x^8^{3/2)}) ?
The first derivative of 3/((3-x^8^{3/2)}) is (36x^7)/((3-x^8)^{5/2)}