What is (\partial)/(\partial b)((a^3b^4)/(c^2d^4)) ?

The answer to (\partial)/(\partial b)((a^3b^4)/(c^2d^4)) is (4a^3b^3)/(c^2d^4)

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(\partial)/(\partial b)((a^3b^4)/(c^2d^4))

\frac{\partial}{\partial b} (\frac{a ^{3} b ^{4}}{c ^{2} d ^{4}})

\frac{4 a ^{3} b ^{3}}{c ^{2} d ^{4}}

Solution steps

\frac{\partial}{\partial b} (\frac{a ^{3} b ^{4}}{c ^{2} d ^{4}})

Take the constant out:

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

= \frac{a ^{3}}{c ^{2} d ^{4}} \frac{\partial}{\partial b} (b^{4})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{a ^{3}}{c ^{2} d ^{4}} \cdot 4 b^{4 - 1}

Simplify

\frac{a ^{3}}{c ^{2} d ^{4}} \cdot 4 b^{4 - 1} : \frac{4 a ^{3} b ^{3}}{c ^{2} d ^{4}}

= \frac{4 a ^{3} b ^{3}}{c ^{2} d ^{4}}

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

\int_{\frac{1}{2}}^{1} (x^{- 3} - 24) d x

y^{^{''}} + 2 y^{^{'}} + y = 2

x \to 0 lim (x \cdot e^{x})

\frac{d}{d x} (\frac{10 lo g _{4} ( x )}{x})

What is (\partial)/(\partial b)((a^3b^4)/(c^2d^4)) ?
The answer to (\partial)/(\partial b)((a^3b^4)/(c^2d^4)) is (4a^3b^3)/(c^2d^4)