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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

2 (x - y) d x + d y = 0

x \to 1 + lim ((x)^{\frac{1}{1 - x}})

x + ∣ x ∣

((x + y)^{2}) d x + (2 x y + x^{2} - 8) d y = 0, y (1) = 1

\frac{\partial}{\partial y} (z)

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