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Popular >

derivative of sec^2(xtan(x))

Solution

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

Solution

- 2 sec^{2} (x) + 3 sec^{4} (x)

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sec^{2} (x), g = tan (x)

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

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

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

= 2 sec^{2} (x) tan (x) tan (x) + sec^{2} (x) sec^{2} (x)

Simplify

2 sec^{2} (x) tan (x) tan (x) + sec^{2} (x) sec^{2} (x) : - 2 sec^{2} (x) + 3 sec^{4} (x)

= - 2 sec^{2} (x) + 3 sec^{4} (x)

Graph

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\int_{6}^{8} \frac{72}{( x - 6 ) ^{3}} d x

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x \to 3 lim (f (x))

(dy)/(dx)=(x^2y^2)/(1+2)

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\int \frac{7 - 98 x}{9 - 49 x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of sec^2(xtan(x)) ?
The derivative of sec^2(xtan(x)) is -2sec^2(x)+3sec^4(x)
What is the first derivative of sec^2(xtan(x)) ?
The first derivative of sec^2(xtan(x)) is -2sec^2(x)+3sec^4(x)