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Popular >

(t/(t+1(sqrt(t))))^'

Solution

(\frac{t}{t + 1 ( t )})^{^{'}}

Solution

\frac{t}{2 ( t + t ) ^{2}}

Solution steps

(\frac{t}{t + 1 \cdot ( t )})^{'}

Apply the Quotient Rule:

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

= \frac{t ^{^{'}} ( t + 1 \cdot t ) - ( t + 1 \cdot t ) ^{^{'}} t}{( t + 1 \cdot t ) ^{2}}

t^{'} = 1

(t + 1 \cdot t)^{'} = 1 + \frac{1}{2 t}

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

Simplify

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

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

Popular Examples

y^'+y/x = 1/(x^2)

y^{^{'}} + \frac{y}{x} = \frac{1}{x ^{2}}

tangent of y=4sin(pix+y),(1,0)tangent of

y = 4 sin (π x + y), (1, 0)

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n = 0 \sum \infty 6 (- \frac{2}{3})^{n}

y^'=(y^4-3)/((4xy^3))

y^{^{'}} = \frac{y ^{4} - 3}{( 4 x y ^{3} )}

limit as x approaches-1 of 4x^2-3x+2

x \to - 1 lim (4 x^{2} - 3 x + 2)

Frequently Asked Questions (FAQ)

What is the (t/(t+1(sqrt(t))))^' ?
The (t/(t+1(sqrt(t))))^' is (sqrt(t))/(2(t+sqrt(t))^2)
What is the first (t/(t+1(sqrt(t))))^' ?
The first (t/(t+1(sqrt(t))))^' is (sqrt(t))/(2(t+sqrt(t))^2)