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Popular >

derivative of (ln(t))/t

Solution

derivative of

\frac{ln ( t )}{t}

Solution

\frac{1 - ln ( t )}{t ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d t} ( ln ( t ) ) t - \frac{d t}{d t} ln ( t )}{t ^{2}}

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

\frac{d t}{d t} = 1

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

Simplify

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

= \frac{1 - ln ( t )}{t ^{2}}

Popular Examples

integral of (sqrt(x^2-256))/x

\int \frac{x ^{2} - 256}{x} d x

area x=-3,x=4,y=e^{2x},y=2e^{-x}area

x = - 3, x = 4, y = e^{2 x}, y = 2 e^{- x}

derivative of x^msqrt(a^2-x^2)

\frac{d}{d x} (x^{m} a^{2} - x^{2})

(\partial)/(\partial x)(x^2+8xy+17y^2-2y+1)

\frac{\partial}{\partial x} (x^{2} + 8 x y + 17 y^{2} - 2 y + 1)

(\partial)/(\partial x)(sin(2t))

\frac{\partial}{\partial x} (sin (2 t))

Frequently Asked Questions (FAQ)

What is the derivative of (ln(t))/t ?
The derivative of (ln(t))/t is (1-ln(t))/(t^2)
What is the first derivative of (ln(t))/t ?
The first derivative of (ln(t))/t is (1-ln(t))/(t^2)