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

The derivative of tan((x^2/(2x+3))) is (sec^2(\frac{x^2)/(2x+3))(2x^2+6x)}{(2x+3)^2}

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

The first derivative of tan((x^2/(2x+3))) is (sec^2(\frac{x^2)/(2x+3))(2x^2+6x)}{(2x+3)^2}

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

\frac{sec ^{2} ( \frac{x ^{2}}{2 x + 3} ) ( 2 x ^{2} + 6 x )}{( 2 x + 3 ) ^{2}}

Solution steps

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

Apply the chain rule:

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

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

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

= sec^{2} (\frac{x ^{2}}{2 x + 3}) \frac{2 x ^{2} + 6 x}{( 2 x + 3 ) ^{2}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{sec ^{2} ( \frac{x ^{2}}{2 x + 3} ) ( 2 x ^{2} + 6 x )}{( 2 x + 3 ) ^{2}}

\int - csc (x) d x

\frac{\partial}{\partial x} (ln (y) + 2 x y^{3})

y^{^{''}} + 9 y = 3 x e^{2 x}

t \to 0 lim (\frac{e ^{5 t} - 1}{t})

\int f^{- 1} (x) d x

What is the derivative of tan((x^2/(2x+3))) ?
The derivative of tan((x^2/(2x+3))) is (sec^2(\frac{x^2)/(2x+3))(2x^2+6x)}{(2x+3)^2}
What is the first derivative of tan((x^2/(2x+3))) ?
The first derivative of tan((x^2/(2x+3))) is (sec^2(\frac{x^2)/(2x+3))(2x^2+6x)}{(2x+3)^2}