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

The derivative of tan((x^2)/3) is (2xsec^2((x^2)/3))/(3)

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

The first derivative of tan((x^2)/3) is (2xsec^2((x^2)/3))/(3)

Popular >

derivative of

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Multiply fractions:

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

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

\frac{d}{d x} (cos^{3} (x) cos^{4} (y) cos^{5} (z))

\frac{x ^{3}}{4 - x}

\frac{1}{4 x ^{2}}

f (x) = 50

y = x (4 x - 3)

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