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Popular >

derivative of f(x)=(x^2)/(cos(x))

Solution

derivative of

f (x) = \frac{x ^{2}}{cos ( x )}

Solution

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

Solution steps

\frac{d}{d x} (\frac{x ^{2}}{cos ( x )})

Simplify

\frac{x ^{2}}{cos ( x )} : x^{2} sec (x)

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = sec (x)

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

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

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

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

Graph

Popular Examples

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

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\int cot (13 x) d x

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\int sin^{3} (x) sin (3 x) d x

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\int \frac{3 sin ( x )}{( 1 + cos ( x ) ) ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(x^2)/(cos(x)) ?
The derivative of f(x)=(x^2)/(cos(x)) is 2xsec(x)+sec(x)tan(x)x^2
What is the first derivative of f(x)=(x^2)/(cos(x)) ?
The first derivative of f(x)=(x^2)/(cos(x)) is 2xsec(x)+sec(x)tan(x)x^2