What is the derivative of ((x+x^9^{-6}+3x)^3) ?

The derivative of ((x+x^9^{-6}+3x)^3) is 3(1/((x+x^9)^6)+3x)^2(-(6(1+9x^8))/((x+x^9)^7)+3)

What is the first derivative of ((x+x^9^{-6}+3x)^3) ?

The first derivative of ((x+x^9^{-6}+3x)^3) is 3(1/((x+x^9)^6)+3x)^2(-(6(1+9x^8))/((x+x^9)^7)+3)

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\frac{d}{d x} (((x + x^{9})^{- 6} + 3 x)^{3})

3 (\frac{1}{( x + x ^{9} ) ^{6}} + 3 x)^{2} (- \frac{6 ( 1 + 9 x ^{8} )}{( x + x ^{9} ) ^{7}} + 3)

Solution steps

\frac{d}{d x} (((x + x^{9})^{- 6} + 3 x)^{3})

Apply the chain rule:

3 ((x + x^{9})^{- 6} + 3 x)^{2} \frac{d}{d x} ((x + x^{9})^{- 6} + 3 x)

= 3 ((x + x^{9})^{- 6} + 3 x)^{2} \frac{d}{d x} ((x + x^{9})^{- 6} + 3 x)

\frac{d}{d x} ((x + x^{9})^{- 6} + 3 x) = - \frac{6 ( 1 + 9 x ^{8} )}{( x + x ^{9} ) ^{7}} + 3

= 3 ((x + x^{9})^{- 6} + 3 x)^{2} (- \frac{6 ( 1 + 9 x ^{8} )}{( x + x ^{9} ) ^{7}} + 3)

Apply exponent rule:

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

= 3 (\frac{1}{( x + x ^{9} ) ^{6}} + 3 x)^{2} (- \frac{6 ( 1 + 9 x ^{8} )}{( x + x ^{9} ) ^{7}} + 3)

\frac{d}{d z} (x z)

4 y y^{^{'}} = x

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

\frac{4}{( s ^{2} - 9 )}

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

What is the derivative of ((x+x^9^{-6}+3x)^3) ?
The derivative of ((x+x^9^{-6}+3x)^3) is 3(1/((x+x^9)^6)+3x)^2(-(6(1+9x^8))/((x+x^9)^7)+3)
What is the first derivative of ((x+x^9^{-6}+3x)^3) ?
The first derivative of ((x+x^9^{-6}+3x)^3) is 3(1/((x+x^9)^6)+3x)^2(-(6(1+9x^8))/((x+x^9)^7)+3)