What is the derivative of ((7x+1/(2x^2+3))^3) ?

The derivative of ((7x+1/(2x^2+3))^3) is (3(7x+1)^2(-14x^2-4x+21))/((2x^2+3)^4)

What is the first derivative of ((7x+1/(2x^2+3))^3) ?

The first derivative of ((7x+1/(2x^2+3))^3) is (3(7x+1)^2(-14x^2-4x+21))/((2x^2+3)^4)

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\frac{d}{d x} ((\frac{7 x + 1}{2 x ^{2} + 3})^{3})

\frac{3 ( 7 x + 1 ) ^{2} ( - 14 x ^{2} - 4 x + 21 )}{( 2 x ^{2} + 3 ) ^{4}}

Solution steps

\frac{d}{d x} ((\frac{7 x + 1}{2 x ^{2} + 3})^{3})

Apply the chain rule:

3 (\frac{7 x + 1}{2 x ^{2} + 3})^{2} \frac{d}{d x} (\frac{7 x + 1}{2 x ^{2} + 3})

= 3 (\frac{7 x + 1}{2 x ^{2} + 3})^{2} \frac{d}{d x} (\frac{7 x + 1}{2 x ^{2} + 3})

\frac{d}{d x} (\frac{7 x + 1}{2 x ^{2} + 3}) = \frac{- 14 x ^{2} - 4 x + 21}{( 2 x ^{2} + 3 ) ^{2}}

= 3 (\frac{7 x + 1}{2 x ^{2} + 3})^{2} \frac{- 14 x ^{2} - 4 x + 21}{( 2 x ^{2} + 3 ) ^{2}}

Simplify

3 (\frac{7 x + 1}{2 x ^{2} + 3})^{2} \frac{- 14 x ^{2} - 4 x + 21}{( 2 x ^{2} + 3 ) ^{2}} : \frac{3 ( 7 x + 1 ) ^{2} ( - 14 x ^{2} - 4 x + 21 )}{( 2 x ^{2} + 3 ) ^{4}}

= \frac{3 ( 7 x + 1 ) ^{2} ( - 14 x ^{2} - 4 x + 21 )}{( 2 x ^{2} + 3 ) ^{4}}

\frac{\partial}{\partial x} (2 x (y - 3 x) - 4 y)

\frac{d}{d x} (\frac{x - 5}{x + 3})

\int \frac{1}{y ^{4} y ^{2} - 5} d y

ln (k x)

y^{^{'}} - 3 y = 2 x + 1

What is the derivative of ((7x+1/(2x^2+3))^3) ?
The derivative of ((7x+1/(2x^2+3))^3) is (3(7x+1)^2(-14x^2-4x+21))/((2x^2+3)^4)
What is the first derivative of ((7x+1/(2x^2+3))^3) ?
The first derivative of ((7x+1/(2x^2+3))^3) is (3(7x+1)^2(-14x^2-4x+21))/((2x^2+3)^4)