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Popular >

derivative of sqrt(tan(x^2))

Solution

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

Solution

x sec^{2} (x^{2}) cot (x^{2})

Solution steps

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

Apply the chain rule:

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

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

Simplify

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

= x sec^{2} (x^{2}) cot (x^{2})

Popular Examples

(\partial)/(\partial y)(x-y^2)

\frac{\partial}{\partial y} (x - y^{2})

derivative of (-cos(4x+1)^2+1)

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

area y=-x^2+4,y=3x area

y = - x^{2} + 4, y = 3 x

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

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

(dy)/(dx)=sqrt(6y)e^{x+9}

\frac{d y}{d x} = 6 y e^{x + 9}

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(tan(x^2)) ?
The derivative of sqrt(tan(x^2)) is xsec^2(x^2)sqrt(cot(x^2))
What is the first derivative of sqrt(tan(x^2)) ?
The first derivative of sqrt(tan(x^2)) is xsec^2(x^2)sqrt(cot(x^2))