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Popular >

derivative of tan(ln(ax+b))

Solution

\frac{d}{d x} (tan (ln (a x + b)))

Solution

\frac{a sec ^{2} ( ln ( a x + b ) )}{a x + b}

Solution steps

\frac{d}{d x} (tan (ln (a x + b)))

Apply the chain rule:

sec^{2} (ln (a x + b)) \frac{d}{d x} (ln (a x + b))

= sec^{2} (ln (a x + b)) \frac{d}{d x} (ln (a x + b))

\frac{d}{d x} (ln (a x + b)) = \frac{a}{a x + b}

= sec^{2} (ln (a x + b)) \frac{a}{a x + b}

Multiply fractions:

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

= \frac{a sec ^{2} ( ln ( a x + b ) )}{a x + b}

Popular Examples

derivative of x^3-1/(x^2)

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

limit as x approaches-infinity of xe^x-1

x \to - \infty lim (x e^{x} - 1)

derivative of (x^3)/(5-x^2)derivative of

\frac{x ^{3}}{5 - x ^{2}}

derivative of 1/3 x^3+7x^2+50x

\frac{d}{d x} (\frac{1}{3} x^{3} + 7 x^{2} + 50 x)

integral of (y^4)/(sqrt(y^2-9))

\int \frac{y ^{4}}{y ^{2} - 9} d y

Frequently Asked Questions (FAQ)

What is the derivative of tan(ln(ax+b)) ?
The derivative of tan(ln(ax+b)) is (asec^2(ln(ax+b)))/(ax+b)
What is the first derivative of tan(ln(ax+b)) ?
The first derivative of tan(ln(ax+b)) is (asec^2(ln(ax+b)))/(ax+b)