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Popular >

derivative of sqrt(x)+4/(sqrt(x)+4)

Solution

\frac{d}{d x} (x + \frac{4}{x} + 4)

Solution

\frac{1}{2 x} - \frac{2}{x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (x + \frac{4}{x} + 4)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x) + \frac{d}{d x} (\frac{4}{x}) + \frac{d}{d x} (4)

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

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

\frac{d}{d x} (4) = 0

= \frac{1}{2 x} - \frac{2}{x ^{\frac{3}{2}}} + 0

Simplify

= \frac{1}{2 x} - \frac{2}{x ^{\frac{3}{2}}}

Popular Examples

integral of (sqrt(25+x^2))/x

\int \frac{25 + x ^{2}}{x} d x

(\partial)/(\partial y)(xsqrt(1+y^7))

\frac{\partial}{\partial y} (x 1 + y^{7})

tangent of f(x)=(6x)/(x+2),\at x=4 tangent of

f (x) = \frac{6 x}{x + 2}, at x = 4

y^{''}-4y^'+4y=e^{2x}

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x}

(5y-2x)dy-2ydx=0

(5 y - 2 x) d y - 2 y d x = 0

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x)+4/(sqrt(x)+4) ?
The derivative of sqrt(x)+4/(sqrt(x)+4) is 1/(2sqrt(x))-2/(x^{3/2)}
What is the first derivative of sqrt(x)+4/(sqrt(x)+4) ?
The first derivative of sqrt(x)+4/(sqrt(x)+4) is 1/(2sqrt(x))-2/(x^{3/2)}