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Popular >

derivative of sec^2(5x^2)

Solution

\frac{d}{d x} (sec^{2} (5 x^{2}))

Solution

20 x sec^{2} (5 x^{2}) tan (5 x^{2})

Solution steps

\frac{d}{d x} (sec^{2} (5 x^{2}))

Apply the chain rule:

2 sec (5 x^{2}) \frac{d}{d x} (sec (5 x^{2}))

= 2 sec (5 x^{2}) \frac{d}{d x} (sec (5 x^{2}))

\frac{d}{d x} (sec (5 x^{2})) = sec (5 x^{2}) tan (5 x^{2}) \cdot 10 x

= 2 sec (5 x^{2}) sec (5 x^{2}) tan (5 x^{2}) \cdot 10 x

Simplify

2 sec (5 x^{2}) sec (5 x^{2}) tan (5 x^{2}) \cdot 10 x : 20 x sec^{2} (5 x^{2}) tan (5 x^{2})

= 20 x sec^{2} (5 x^{2}) tan (5 x^{2})

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\int_{0}^{1} 2 π x (x^{5} - x^{6}) d x

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\int \frac{1}{e ^{2 y}} d y

x(dy)/(dx)+2y=x^3-x

x \frac{d y}{d x} + 2 y = x^{3} - x

integral from 0 to pi of tcos^2(t)

\int_{0}^{π} t cos^{2} (t) d t

Frequently Asked Questions (FAQ)

What is the derivative of sec^2(5x^2) ?
The derivative of sec^2(5x^2) is 20xsec^2(5x^2)tan(5x^2)
What is the first derivative of sec^2(5x^2) ?
The first derivative of sec^2(5x^2) is 20xsec^2(5x^2)tan(5x^2)