What is (\partial)/(\partial x)(1/4 (x+y)^4) ?

The answer to (\partial)/(\partial x)(1/4 (x+y)^4) is (x+y)^3

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(\partial)/(\partial x)(1/4 (x+y)^4)

\frac{\partial}{\partial x} (\frac{1}{4} (x + y)^{4})

(x + y)^{3}

Solution steps

\frac{\partial}{\partial x} (\frac{1}{4} (x + y)^{4})

Treat

y

as a constant

Take the constant out:

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

= \frac{1}{4} \frac{\partial}{\partial x} ((x + y)^{4})

Apply the chain rule:

4 (x + y)^{3} \frac{\partial}{\partial x} (x + y)

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

\frac{\partial}{\partial x} (x + y) = 1

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

Simplify

\frac{1}{4} \cdot 4 (x + y)^{3} \cdot 1 : (x + y)^{3}

= (x + y)^{3}

What is (\partial)/(\partial x)(1/4 (x+y)^4) ?
The answer to (\partial)/(\partial x)(1/4 (x+y)^4) is (x+y)^3