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Popular >

derivative of 1/3 tan^3(x-tan(x)+x)

Solution

\frac{d}{d x} (\frac{1}{3} tan^{3} (x) - tan (x) + x)

Solution

tan^{4} (x)

Solution steps

\frac{d}{d x} (\frac{1}{3} tan^{3} (x) - tan (x) + x)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{3} tan^{3} (x)) - \frac{d}{d x} (tan (x)) + \frac{d x}{d x}

\frac{d}{d x} (\frac{1}{3} tan^{3} (x)) = tan^{2} (x) sec^{2} (x)

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

\frac{d x}{d x} = 1

= tan^{2} (x) sec^{2} (x) - sec^{2} (x) + 1

Simplify

tan^{2} (x) sec^{2} (x) - sec^{2} (x) + 1 : tan^{4} (x)

= tan^{4} (x)

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Frequently Asked Questions (FAQ)

What is the derivative of 1/3 tan^3(x-tan(x)+x) ?
The derivative of 1/3 tan^3(x-tan(x)+x) is tan^4(x)
What is the first derivative of 1/3 tan^3(x-tan(x)+x) ?
The first derivative of 1/3 tan^3(x-tan(x)+x) is tan^4(x)