What is (\partial)/(\partial x)(4/(sqrt(36-x^2))) ?

The answer to (\partial)/(\partial x)(4/(sqrt(36-x^2))) is (4x)/((36-x^2)^{3/2)}

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(\partial)/(\partial x)(4/(sqrt(36-x^2)))

\frac{\partial}{\partial x} (\frac{4}{36 - x ^{2}})

\frac{4 x}{( 36 - x ^{2} ) ^{\frac{3}{2}}}

Solution steps

\frac{\partial}{\partial x} (\frac{4}{36 - x ^{2}})

Take the constant out:

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

= 4 \frac{\partial}{\partial x} (\frac{1}{36 - x ^{2}})

Apply exponent rule:

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

= 4 \frac{\partial}{\partial x} ((36 - x^{2})^{- \frac{1}{2}})

Apply the chain rule:

- \frac{1}{2 ( 36 - x ^{2} ) ^{\frac{3}{2}}} \frac{\partial}{\partial x} (36 - x^{2})

= - \frac{1}{2 ( 36 - x ^{2} ) ^{\frac{3}{2}}} \frac{\partial}{\partial x} (36 - x^{2})

\frac{\partial}{\partial x} (36 - x^{2}) = - 2 x

= 4 (- \frac{1}{2 ( 36 - x ^{2} ) ^{\frac{3}{2}}} (- 2 x))

Simplify

4 (- \frac{1}{2 ( 36 - x ^{2} ) ^{\frac{3}{2}}} (- 2 x)) : \frac{4 x}{( 36 - x ^{2} ) ^{\frac{3}{2}}}

= \frac{4 x}{( 36 - x ^{2} ) ^{\frac{3}{2}}}

(2) (- 3.1)

\int cos^{7} (8 - x) sin (8 - x) d x

y^{^{'}} - 4 y = 9 e^{7 t}

\int tan^{2} (8 x) sec^{4} (8 x) d x

\int y^{2} 4 y^{2} + 1 d y

What is (\partial)/(\partial x)(4/(sqrt(36-x^2))) ?
The answer to (\partial)/(\partial x)(4/(sqrt(36-x^2))) is (4x)/((36-x^2)^{3/2)}