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Popular >

derivative of f(x)=tan(ln(ax+b))

Solution

derivative of

f (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

(\partial)/(\partial x)(y+sin(x))

\frac{\partial}{\partial x} (y + sin (x))

derivative of 8e^{3x}derivative of

8 e^{3 x}

integral of+(2x+1)/((x+5)^3)

\int + \frac{2 x + 1}{( x + 5 ) ^{3}} d x

x*(dy)/(dx)+5y=7x^2

x \cdot \frac{d y}{d x} + 5 y = 7 x^{2}

derivative of 1/(\sqrt[3]{x^2+x+3})

Frequently Asked Questions (FAQ)

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