What is (\partial)/(\partial x)((2x+1)^y) ?

The answer to (\partial)/(\partial x)((2x+1)^y) is y(2x+1)^{y-1}*2

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(\partial)/(\partial x)((2x+1)^y)

\frac{\partial}{\partial x} ((2 x + 1)^{y})

y (2 x + 1)^{y - 1} \cdot 2

Solution steps

\frac{\partial}{\partial x} ((2 x + 1)^{y})

Treat

y

as a constant

Apply the chain rule:

y (2 x + 1)^{y - 1} \frac{\partial}{\partial x} (2 x + 1)

= y (2 x + 1)^{y - 1} \frac{\partial}{\partial x} (2 x + 1)

\frac{\partial}{\partial x} (2 x + 1) = 2

= y (2 x + 1)^{y - 1} \cdot 2

\frac{d}{d x} (tan (5 x^{2} - x))

\int 10 csc^{2} (5 x) cot (5 x) d x

\frac{\partial}{\partial x} (\frac{sin ( x + y )}{y ^{2}})

4 \frac{d y}{d x} - 12 x^{2} = 0

y = \frac{80}{x ^{6}}

What is (\partial)/(\partial x)((2x+1)^y) ?
The answer to (\partial)/(\partial x)((2x+1)^y) is y(2x+1)^{y-1}*2