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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)

Popular Examples

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\frac{d}{d x} (g (h, x) (h (x)))

integral of (cos(x))/(7+sin^2(x))

\int \frac{cos ( x )}{7 + sin ^{2} ( x )} d x

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2 - ∣ x ∣, x^{2}

(dy}{dx}+\frac{2y)/x = 9/x

\frac{d y}{d x} + \frac{2 y}{x} = \frac{9}{x}

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)