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Popular >

derivative of f(x)=ln(3+sqrt(x))

Solution

derivative of

f (x) = ln (3 + x)

Solution

\frac{1}{2 x ( 3 + x )}

Solution steps

\frac{d}{d x} (ln (3 + x))

Apply the chain rule:

\frac{1}{3 + x} \frac{d}{d x} (3 + x)

= \frac{1}{3 + x} \frac{d}{d x} (3 + x)

\frac{d}{d x} (3 + x) = \frac{1}{2 x}

= \frac{1}{3 + x} \cdot \frac{1}{2 x}

Simplify

\frac{1}{3 + x} \cdot \frac{1}{2 x} : \frac{1}{2 x ( 3 + x )}

= \frac{1}{2 x ( 3 + x )}

Popular Examples

(dy)/(dx)=(y^2+6xsqrt(x^2+y^2))/(xy)

\frac{d y}{d x} = \frac{y ^{2} + 6 x x ^{2} + y ^{2}}{x y}

tangent of f(x)=2(x^2-1)^3,\at x=2 tangent of

f (x) = 2 (x^{2} - 1)^{3}, at x = 2

limit as x approaches-8+of (2x)/(x+8)

x \to - 8 + lim (\frac{2 x}{x + 8})

derivative of f(x)= 2/(sqrt(4x+3))derivative of

f (x) = \frac{2}{4 x + 3}

derivative of f(x)=(1-3x)/(1+3x)derivative of

f (x) = \frac{1 - 3 x}{1 + 3 x}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=ln(3+sqrt(x)) ?
The derivative of f(x)=ln(3+sqrt(x)) is 1/(2sqrt(x)(3+\sqrt{x))}
What is the first derivative of f(x)=ln(3+sqrt(x)) ?
The first derivative of f(x)=ln(3+sqrt(x)) is 1/(2sqrt(x)(3+\sqrt{x))}