What is the d/(dt)((tsin(t))/(1+t)) ?

The d/(dt)((tsin(t))/(1+t)) is (t^2cos(t)+tcos(t)+sin(t))/((1+t)^2)

What is the first d/(dt)((tsin(t))/(1+t)) ?

The first d/(dt)((tsin(t))/(1+t)) is (t^2cos(t)+tcos(t)+sin(t))/((1+t)^2)

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

\frac{t ^{2} cos ( t ) + t cos ( t ) + sin ( t )}{( 1 + t ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d t} (t sin (t)) = sin (t) + t cos (t)

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

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

Simplify

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

= \frac{t ^{2} cos ( t ) + t cos ( t ) + sin ( t )}{( 1 + t ) ^{2}}

\int 0.1 x^{2} d x

\int \frac{6}{x ^{2} - x - 2} d x

y^{^{'}} (1 - x y^{1985}) = y^{1986}

\int \frac{5 x ^{3} - 3 x}{x} d x

\int_{22}^{4} \frac{1}{t ^{3} t ^{2} - 4} d t

What is the d/(dt)((tsin(t))/(1+t)) ?
The d/(dt)((tsin(t))/(1+t)) is (t^2cos(t)+tcos(t)+sin(t))/((1+t)^2)
What is the first d/(dt)((tsin(t))/(1+t)) ?
The first d/(dt)((tsin(t))/(1+t)) is (t^2cos(t)+tcos(t)+sin(t))/((1+t)^2)