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Popular >

derivative of y=sqrt(tan(2x))

Solution

derivative of

y = tan (2 x)

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

integral of ((x))/((4x^{(2))-12x+25)}

\int \frac{( x )}{( 4 x ^{(2)} - 12 x + 25 )} d x

limit as x approaches 0+of 1/(1-cos(x))

x \to 0 + lim (\frac{1}{1 - cos ( x )})

limit as x approaches 4 of (x-5)/((x-4)^2)

x \to 4 lim (\frac{x - 5}{( x - 4 ) ^{2}})

xy^'+2y=-4sin(x)

x y^{^{'}} + 2 y = - 4 sin (x)

tangent of 2x^2+xy+2y^2=5,(1,1)tangent of

2 x^{2} + x y + 2 y^{2} = 5, (1, 1)

Frequently Asked Questions (FAQ)

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