What is the derivative of 8/(sqrt((x^3+x^2+1^3))) ?

The derivative of 8/(sqrt((x^3+x^2+1^3))) is -(12(3x^2+2x))/((x^3+x^2+1)^{5/2)}

What is the first derivative of 8/(sqrt((x^3+x^2+1^3))) ?

The first derivative of 8/(sqrt((x^3+x^2+1^3))) is -(12(3x^2+2x))/((x^3+x^2+1)^{5/2)}

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

- \frac{12 ( 3 x ^{2} + 2 x )}{( x ^{3} + x ^{2} + 1 ) ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the chain rule:

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

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

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

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

Simplify

8 - \frac{1}{2 ( ( x ^{3} + x ^{2} + 1 ) ^{3} ) ^{\frac{3}{2}}} \cdot 3 (x^{3} + x^{2} + 1)^{2} (3 x^{2} + 2 x) : - \frac{12 ( 3 x ^{2} + 2 x )}{( x ^{3} + x ^{2} + 1 ) ^{\frac{5}{2}}}

= - \frac{12 ( 3 x ^{2} + 2 x )}{( x ^{3} + x ^{2} + 1 ) ^{\frac{5}{2}}}

\int sin (a x) d x

y = \frac{2 x - sin ( 2 x )}{x ^{2} + cos ( x ^{2} )}

\int \frac{( 1 0 ^{2 x} + 1 )}{( 1 0 ^{x} - 1 )} d x

\int \frac{( x ^{2} - 16 )}{( x - 4 )} d x

\int_{2}^{4} \frac{1}{x} d x

What is the derivative of 8/(sqrt((x^3+x^2+1^3))) ?
The derivative of 8/(sqrt((x^3+x^2+1^3))) is -(12(3x^2+2x))/((x^3+x^2+1)^{5/2)}
What is the first derivative of 8/(sqrt((x^3+x^2+1^3))) ?
The first derivative of 8/(sqrt((x^3+x^2+1^3))) is -(12(3x^2+2x))/((x^3+x^2+1)^{5/2)}