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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

\frac{d}{d x} (x^{4} + 2 x)

\frac{1}{4 x}

\int_{4}^{9} \frac{x - x}{x} d x

\int 3 \cdot x + 4 d x

n = 0 \sum \infty \frac{4}{n ^{2}}

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