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Popular >

derivative of t/(t-1)

Solution

derivative of

\frac{t}{t - 1}

Solution

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

Solution steps

\frac{d}{d t} (\frac{t}{t - 1})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

(1+cos(t))y^'=(1+e-y)sin(t)

(1 + cos (t)) y^{^{'}} = (1 + e - y) sin (t)

y^{''}+4y=8tan(2x)

y^{^{''}} + 4 y = 8 tan (2 x)

integral of (sqrt(x^2+4x+3))/(x+2)

\int \frac{x ^{2} + 4 x + 3}{x + 2} d x

integral of e^xsqrt(49+e^x)

\int e^{x} 49 + e^{x} d x

y^{''}+2y=-18x^2e^{2x}

y^{^{''}} + 2 y = - 18 x^{2} e^{2 x}

Frequently Asked Questions (FAQ)

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