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Popular Calculus >

derivative of sec^2(x+csc^2(x))

Solution

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

Solution

2 sec^{2} (x) tan (x) - 2 csc^{2} (x) cot (x)

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (csc^{2} (x)) = - 2 csc^{2} (x) cot (x)

= 2 sec^{2} (x) tan (x) - 2 csc^{2} (x) cot (x)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of sec^2(x+csc^2(x)) ?
The derivative of sec^2(x+csc^2(x)) is 2sec^2(x)tan(x)-2csc^2(x)cot(x)
What is the first derivative of sec^2(x+csc^2(x)) ?
The first derivative of sec^2(x+csc^2(x)) is 2sec^2(x)tan(x)-2csc^2(x)cot(x)