What is the derivative of arctan((a^2-x^3/(b^2))) ?

The derivative of arctan((a^2-x^3/(b^2))) is -(3b^2x^2)/((-x^3+a^2)^2+b^4)

What is the first derivative of arctan((a^2-x^3/(b^2))) ?

The first derivative of arctan((a^2-x^3/(b^2))) is -(3b^2x^2)/((-x^3+a^2)^2+b^4)

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\frac{d}{d x} (arctan (\frac{a ^{2} - x ^{3}}{b ^{2}}))

- \frac{3 b ^{2} x ^{2}}{( - x ^{3} + a ^{2} ) ^{2} + b ^{4}}

Solution steps

\frac{d}{d x} (arctan (\frac{a ^{2} - x ^{3}}{b ^{2}}))

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{( \frac{a ^{2} - x ^{3}}{b ^{2}} ) ^{2} + 1} (- \frac{3 x ^{2}}{b ^{2}}) : - \frac{3 b ^{2} x ^{2}}{( - x ^{3} + a ^{2} ) ^{2} + b ^{4}}

= - \frac{3 b ^{2} x ^{2}}{( - x ^{3} + a ^{2} ) ^{2} + b ^{4}}

\int_{1}^{\infty} \frac{x}{x ^{2} + 1} d x

\frac{\partial}{\partial y} (x y^{2} e^{x^{2}})

x \to - 1 - lim (2 x^{2} - 4 x + 8)

\frac{\partial}{\partial x} (6 x y + 5 yz + x z - 48)

16 y^{^{''}} + 152 y^{^{'}} + 361 y = 0, y (0) = 9, y^{^{'}} (0) = 2

What is the derivative of arctan((a^2-x^3/(b^2))) ?
The derivative of arctan((a^2-x^3/(b^2))) is -(3b^2x^2)/((-x^3+a^2)^2+b^4)
What is the first derivative of arctan((a^2-x^3/(b^2))) ?
The first derivative of arctan((a^2-x^3/(b^2))) is -(3b^2x^2)/((-x^3+a^2)^2+b^4)