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Popular Calculus >

derivative of tan(x^2+tan^2(x))

Solution

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

Solution

sec^{2} (x^{2}) \cdot 2 x + 2 tan (x) sec^{2} (x)

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

Graph

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Frequently Asked Questions (FAQ)

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