What is (\partial}{\partial x}((2t)/((1-\frac{0.5(x))/L)^2)) ?

The answer to (\partial}{\partial x}((2t)/((1-\frac{0.5(x))/L)^2)) is (2L^2t)/((L-0.5x)^3)

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(\partial}{\partial x}((2t)/((1-\frac{0.5(x))/L)^2))

\frac{\partial}{\partial x} \frac{2 t}{( 1 - \frac{0.5 ( x )}{L} ) ^{2}}

\frac{2 L ^{2} t}{( L - 0.5 x ) ^{3}}

Solution steps

\frac{\partial}{\partial x} \frac{2 t}{( 1 - \frac{0.5 ( x )}{L} ) ^{2}}

Treat

t

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 t \frac{\partial}{\partial x} (\frac{1}{( 1 - \frac{0.5 x}{L} ) ^{2}})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 2 t \frac{\partial}{\partial x} ((1 - \frac{0.5 x}{L})^{- 2})

Apply the chain rule:

- \frac{2}{( 1 - \frac{0.5 x}{L} ) ^{3}} \frac{\partial}{\partial x} (1 - \frac{0.5 x}{L})

= - \frac{2}{( 1 - \frac{0.5 x}{L} ) ^{3}} \frac{\partial}{\partial x} (1 - \frac{0.5 x}{L})

\frac{\partial}{\partial x} (1 - \frac{0.5 x}{L}) = - \frac{0.5}{L}

= 2 t (- \frac{2}{( 1 - \frac{0.5 x}{L} ) ^{3}} (- \frac{0.5}{L}))

Simplify

2 t (- \frac{2}{( 1 - \frac{0.5 x}{L} ) ^{3}} (- \frac{0.5}{L})) : \frac{2 L ^{2} t}{( L - 0.5 x ) ^{3}}

= \frac{2 L ^{2} t}{( L - 0.5 x ) ^{3}}

\frac{d}{d x} (\frac{1}{csc ( x ) + cot ( x )})

2 arcsin (x^{3})

\frac{d}{d x} (10 e^{- 2 x})

h (t) = (t + 5)^{\frac{2}{3}} (3 t^{2} - 5)^{3}

x \to 9 lim (\frac{5}{( x - 9 )})

What is (\partial}{\partial x}((2t)/((1-\frac{0.5(x))/L)^2)) ?
The answer to (\partial}{\partial x}((2t)/((1-\frac{0.5(x))/L)^2)) is (2L^2t)/((L-0.5x)^3)