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Popular >

derivative of (t^2)/(t-2)

Solution

derivative of

\frac{t ^{2}}{t - 2}

Solution

\frac{t ^{2} - 4 t}{( t - 2 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 t ( t - 2 ) - 1 \cdot t ^{2}}{( t - 2 ) ^{2}} : \frac{t ^{2} - 4 t}{( t - 2 ) ^{2}}

= \frac{t ^{2} - 4 t}{( t - 2 ) ^{2}}

Popular Examples

integral of (6x^5+7x)

\int (6 x^{5} + 7 x) d x

integral of xsqrt(-x^2+x)

\int x - x^{2} + x d x

(dy)/(dx)=(y^2)/(e^x),y(0)=-2

\frac{d y}{d x} = \frac{y ^{2}}{e ^{x}}, y (0) = - 2

tangent of y=x^2,(0,-4)tangent of

y = x^{2}, (0, - 4)

limit as x approaches infinity of (sqrt(x))/(ln(x))

x \to \infty lim (\frac{x}{ln ( x )})

Frequently Asked Questions (FAQ)

What is the derivative of (t^2)/(t-2) ?
The derivative of (t^2)/(t-2) is (t^2-4t)/((t-2)^2)
What is the first derivative of (t^2)/(t-2) ?
The first derivative of (t^2)/(t-2) is (t^2-4t)/((t-2)^2)