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Popular >

derivative of g(t)=sqrt(1+ln(t))

Solution

derivative of

g (t) = 1 + ln (t)

Solution

\frac{1}{2 t 1 + ln ( t )}

Solution steps

\frac{d}{d t} (1 + ln (t))

Apply the chain rule:

\frac{1}{2 1 + ln ( t )} \frac{d}{d t} (1 + ln (t))

= \frac{1}{2 1 + ln ( t )} \frac{d}{d t} (1 + ln (t))

\frac{d}{d t} (1 + ln (t)) = \frac{1}{t}

= \frac{1}{2 1 + ln ( t )} \cdot \frac{1}{t}

Simplify

\frac{1}{2 1 + ln ( t )} \cdot \frac{1}{t} : \frac{1}{2 t 1 + ln ( t )}

= \frac{1}{2 t 1 + ln ( t )}

Popular Examples

tangent of f(x)=x^3,\at x=4 tangent of

f (x) = x^{3}, at x = 4

(\partial)/(\partial x)((yx)/(1+yx))

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

integral of 1/((x^2+36)^2)

\int \frac{1}{( x ^{2} + 36 ) ^{2}} d x

laplacetransform 4t^3-24t+24sin(t)laplace transform

4 t^{3} - 24 t + 24 sin (t)

limit as x approaches 1 of-f(x)

x \to 1 lim (- f (x))

Frequently Asked Questions (FAQ)

What is the derivative of g(t)=sqrt(1+ln(t)) ?
The derivative of g(t)=sqrt(1+ln(t)) is 1/(2tsqrt(1+ln(t)))
What is the first derivative of g(t)=sqrt(1+ln(t)) ?
The first derivative of g(t)=sqrt(1+ln(t)) is 1/(2tsqrt(1+ln(t)))