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Popular Calculus >

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

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x^{2} + x, g = tan (x)

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

\frac{d}{d x} (x^{2} + x) = 2 x + 1

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

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

Graph

Popular Examples

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\frac{d}{d x} (arcsin (- x))

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\frac{d}{d x} (6 sec (x^{2}))

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\frac{d}{d x} (\frac{4 - 3 x - x ^{2}}{x - 2})

limit as x approaches-1 of F(x)

x \to - 1 lim (F (x))

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+x*(tan(x))) ?
The derivative of (x^2+x*(tan(x))) is (2x+1)tan(x)+sec^2(x)(x^2+x)
What is the first derivative of (x^2+x*(tan(x))) ?
The first derivative of (x^2+x*(tan(x))) is (2x+1)tan(x)+sec^2(x)(x^2+x)