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Popular >

derivative of ln(tan(x^2))

Solution

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

Solution

4 x csc (2 x^{2})

Solution steps

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

Apply the chain rule:

\frac{1}{tan ( x ^{2} )} \frac{d}{d x} (tan (x^{2}))

= \frac{1}{tan ( x ^{2} )} \frac{d}{d x} (tan (x^{2}))

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

= \frac{1}{tan ( x ^{2} )} sec^{2} (x^{2}) \cdot 2 x

Simplify

\frac{1}{tan ( x ^{2} )} sec^{2} (x^{2}) \cdot 2 x : 4 x csc (2 x^{2})

= 4 x csc (2 x^{2})

Popular Examples

derivative of arctan(x+x-1)

\frac{d}{d x} (arctan (x) + x - 1)

y^{''}-16y^'+73=0,y(0)=6,y^'(0)=6

y^{^{''}} - 16 y^{^{'}} + 73 = 0, y (0) = 6, y^{^{'}} (0) = 6

derivative of 1/2 (4x^2+x^{-3})

\frac{d}{d x} (\frac{1}{2} (4 x^{2} + x)^{- 3})

y^{^{'}} = - 3 y

(\partial)/(\partial x)(e^{6x+4y})

\frac{\partial}{\partial x} (e^{6 x + 4 y})

Frequently Asked Questions (FAQ)

What is the derivative of ln(tan(x^2)) ?
The derivative of ln(tan(x^2)) is 4xcsc(2x^2)
What is the first derivative of ln(tan(x^2)) ?
The first derivative of ln(tan(x^2)) is 4xcsc(2x^2)