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Popular >

derivative of tan^3(x+tan(x^3))

Solution

\frac{d}{d x} (tan^{3} (x) + tan (x^{3}))

Solution

3 tan^{2} (x) sec^{2} (x) + sec^{2} (x^{3}) \cdot 3 x^{2}

Solution steps

\frac{d}{d x} (tan^{3} (x) + tan (x^{3}))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (tan^{3} (x)) + \frac{d}{d x} (tan (x^{3}))

\frac{d}{d x} (tan^{3} (x)) = 3 tan^{2} (x) sec^{2} (x)

\frac{d}{d x} (tan (x^{3})) = sec^{2} (x^{3}) \cdot 3 x^{2}

= 3 tan^{2} (x) sec^{2} (x) + sec^{2} (x^{3}) \cdot 3 x^{2}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of tan^3(x+tan(x^3)) ?
The derivative of tan^3(x+tan(x^3)) is 3tan^2(x)sec^2(x)+sec^2(x^3)*3x^2
What is the first derivative of tan^3(x+tan(x^3)) ?
The first derivative of tan^3(x+tan(x^3)) is 3tan^2(x)sec^2(x)+sec^2(x^3)*3x^2