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Popular >

derivative of xsin(xtan(x))

Solution

\frac{d}{d x} (x sin (x) tan (x))

Solution

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

Solution steps

\frac{d}{d x} (x sin (x) tan (x))

Apply the Product Rule:

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

f = x, g = sin (x) tan (x)

= \frac{d x}{d x} sin (x) tan (x) + \frac{d}{d x} (sin (x) tan (x)) x

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

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

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

Simplify

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

Popular Examples

derivative of (x^{3/2}-4x(x^4-3/(x^2)+2))

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

derivative of sqrt(4x+2)derivative of

4 x + 2

derivative of (2x^2+5x+8/(2x^2))

\frac{d}{d x} (\frac{2 x ^{2} + 5 x + 8}{2 x ^{2}})

integral of 1/((sec(x))^2)

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

derivative of f(x)=3e^x derivative of

f (x) = 3 e^{x}

Frequently Asked Questions (FAQ)

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