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Popular >

derivative of (tan(x))(sqrt(x))

Solution

derivative of

(tan (x)) (x)

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = tan (x), g = x

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

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

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

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

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

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

Graph

Popular Examples

(\partial)/(\partial x)(ln(2x+5y))

\frac{\partial}{\partial x} (ln (2 x + 5 y))

y^{''}+2y^'+3/4 y=0

y^{^{''}} + 2 y^{^{'}} + \frac{3}{4} y = 0

integral of 3-1/(x^4)

\int 3 - \frac{1}{x ^{4}} d x

(ln (1))^{^{'}}

derivative of (sqrt(x)-7/(sqrt(x)+1))

\frac{d}{d x} (\frac{x - 7}{x + 1})

Frequently Asked Questions (FAQ)

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