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Popular >

derivative of sqrt(x/a)

Solution

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

Solution

\frac{1}{2 a x}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 \frac{x}{a}} \cdot \frac{1}{a}

Simplify

\frac{1}{2 \frac{x}{a}} \cdot \frac{1}{a} : \frac{1}{2 a x}

= \frac{1}{2 a x}

Popular Examples

limit as x approaches 0+of ln(arcsin(x))

x \to 0 + lim (ln (arcsin (x)))

limit as x approaches (7pi)/2 of sec(x)

x \to \frac{7 π}{2} lim (sec (x))

tangent of f(x)=(1+4x)(5-2x),\at x=2 tangent of

f (x) = (1 + 4 x) (5 - 2 x), at x = 2

(\partial)/(\partial y)(x^2+3y^2)

\frac{\partial}{\partial y} (x^{2} + 3 y^{2})

tangent of f(x)=sin(sin(x)),0,\at x=pi tangent of

f (x) = sin (sin (x)), 0, at x = π

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x/a) ?
The derivative of sqrt(x/a) is 1/(2sqrt(a)\sqrt{x)}
What is the first derivative of sqrt(x/a) ?
The first derivative of sqrt(x/a) is 1/(2sqrt(a)\sqrt{x)}