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Popular >

derivative of sqrt(x)tan(x)

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = tan (x)

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

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

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

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

\frac{1}{2 x} tan (x) = \frac{tan ( x )}{2 x}

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

Popular Examples

integral of 1/(9+4x^2)

\int \frac{1}{9 + 4 x ^{2}} d x

integral of 2/5-9/x

\int \frac{2}{5} - \frac{9}{x} d x

xdy-(y+x^3e^{x^2})dx=0

x d y - (y + x^{3} e^{x^{2}}) d x = 0

integral of cot(10x)csc^4(10x)

\int cot (10 x) csc^{4} (10 x) d x

(d^2)/(dx^2)((x^2+5)^7)

\frac{d ^{2}}{d x ^{2}} ((x^{2} + 5)^{7})

Frequently Asked Questions (FAQ)

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