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}}

\frac{d}{d x} (\frac{1 - 2 x ^{2}}{x ^{4} - 2 x ^{2} + 6})

\int 1 + (4 x)^{2} d x

\frac{d}{d t} (2 t e^{- t})

\int \frac{1}{sin ( x ) cos ^{2} ( x )} d x

f (x) = 10 sin (x) + 103 cos (x)

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)