What is the derivative of t/((1-t^2)^{3/2)} ?

The derivative of t/((1-t^2)^{3/2)} is (2t^2+1)/((1-t^2)^{5/2)}

What is the first derivative of t/((1-t^2)^{3/2)} ?

The first derivative of t/((1-t^2)^{3/2)} is (2t^2+1)/((1-t^2)^{5/2)}

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derivative of

\frac{t}{( 1 - t ^{2} ) ^{\frac{3}{2}}}

\frac{2 t ^{2} + 1}{( 1 - t ^{2} ) ^{\frac{5}{2}}}

Solution steps

\frac{d}{d t} (\frac{t}{( 1 - t ^{2} ) ^{\frac{3}{2}}})

Apply the Quotient Rule:

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

= \frac{\frac{d t}{d t} ( 1 - t ^{2} ) ^{\frac{3}{2}} - \frac{d}{d t} ( ( 1 - t ^{2} ) ^{\frac{3}{2}} ) t}{( ( 1 - t ^{2} ) ^{\frac{3}{2}} ) ^{2}}

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

\frac{d}{d t} ((1 - t^{2})^{\frac{3}{2}}) = - 3 t (1 - t^{2})^{\frac{1}{2}}

= \frac{1 \cdot ( 1 - t ^{2} ) ^{\frac{3}{2}} - ( - 3 t ( 1 - t ^{2} ) ^{\frac{1}{2}} ) t}{( ( 1 - t ^{2} ) ^{\frac{3}{2}} ) ^{2}}

Simplify

\frac{1 \cdot ( 1 - t ^{2} ) ^{\frac{3}{2}} - ( - 3 t ( 1 - t ^{2} ) ^{\frac{1}{2}} ) t}{( ( 1 - t ^{2} ) ^{\frac{3}{2}} ) ^{2}} : \frac{2 t ^{2} + 1}{( 1 - t ^{2} ) ^{\frac{5}{2}}}

= \frac{2 t ^{2} + 1}{( 1 - t ^{2} ) ^{\frac{5}{2}}}

(2 y - 3 x) \frac{d y}{d x} = 3 y - 4 x

\int_{- \infty}^{0} e^{- ∣ x ∣} d x

\frac{\partial}{\partial y} (x e^{2 y x})

\frac{\partial}{\partial y} (2 + x ln (x y - 5))

\int \frac{1}{x ^{2} - 8 x - 12} d x

What is the derivative of t/((1-t^2)^{3/2)} ?
The derivative of t/((1-t^2)^{3/2)} is (2t^2+1)/((1-t^2)^{5/2)}
What is the first derivative of t/((1-t^2)^{3/2)} ?
The first derivative of t/((1-t^2)^{3/2)} is (2t^2+1)/((1-t^2)^{5/2)}