What is the derivative of xy^4 ?

The derivative of xy^4 is y^4+4xy^3(dy)/(dx)

What is the first derivative of xy^4 ?

The first derivative of xy^4 is y^4+4xy^3(dy)/(dx)

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\frac{d}{d x} (x y^{4})

y^{4} + 4 x y^{3} \frac{d y}{d x}

Solution steps

\frac{d}{d x} (x y^{4})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = y^{4}

= \frac{d x}{d x} y^{4} + \frac{d}{d x} (y^{4}) x

\frac{d x}{d x} = 1

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

= 1 \cdot y^{4} + 4 y^{3} \frac{d y}{d x} x

Simplify

= y^{4} + 4 x y^{3} \frac{d y}{d x}

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What is the derivative of xy^4 ?
The derivative of xy^4 is y^4+4xy^3(dy)/(dx)
What is the first derivative of xy^4 ?
The first derivative of xy^4 is y^4+4xy^3(dy)/(dx)