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Popular >

derivative of 1/(2sqrt(x)+5cos(x))

Solution

\frac{d}{d x} (\frac{1}{2 x} + 5 cos (x))

Solution

- \frac{1}{4 x ^{\frac{3}{2}}} - 5 sin (x)

Solution steps

\frac{d}{d x} (\frac{1}{2 x} + 5 cos (x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{1}{2 x}) + \frac{d}{d x} (5 cos (x))

\frac{d}{d x} (\frac{1}{2 x}) = - \frac{1}{4 x ^{\frac{3}{2}}}

\frac{d}{d x} (5 cos (x)) = - 5 sin (x)

= - \frac{1}{4 x ^{\frac{3}{2}}} - 5 sin (x)

Popular Examples

derivative of-x^2+6x-4

\frac{d}{d x} (- x^{2} + 6 x - 4)

integral of nx^n

\int n x^{n} d x

integral of 1/(x^2sqrt(3-x^2))

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

limit as x approaches infinity of-2x

x \to \infty lim (- 2 x)

(sqrt(2x^4+1))/y (dy)/(dx)+1/6 y^3x^3=0

\frac{2 x ^{4} + 1}{y} \frac{d y}{d x} + \frac{1}{6} y^{3} x^{3} = 0

Frequently Asked Questions (FAQ)

What is the derivative of 1/(2sqrt(x)+5cos(x)) ?
The derivative of 1/(2sqrt(x)+5cos(x)) is -1/(4x^{3/2)}-5sin(x)
What is the first derivative of 1/(2sqrt(x)+5cos(x)) ?
The first derivative of 1/(2sqrt(x)+5cos(x)) is -1/(4x^{3/2)}-5sin(x)