What is (\partial)/(\partial x)(y^{2x}) ?

The answer to (\partial)/(\partial x)(y^{2x}) is 2y^{2x}ln(y)

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(\partial)/(\partial x)(y^{2x})

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

2 y^{2 x} ln (y)

Solution steps

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

Treat

y

as a constant

Apply exponent rule:

a^{b} = e^{b l n (a)}

y^{2 x} = e^{2 x l n (y)}

= \frac{\partial}{\partial x} (e^{2 x l n (y)})

Apply the chain rule:

e^{2 x l n (y)} \frac{\partial}{\partial x} (2 x ln (y))

= e^{2 x l n (y)} \frac{\partial}{\partial x} (2 x ln (y))

\frac{\partial}{\partial x} (2 x ln (y)) = 2 ln (y)

= e^{2 x l n (y)} \cdot 2 ln (y)

e^{2 x l n (y)} = y^{2 x}

= 2 y^{2 x} ln (y)

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

x \to 1 lim (2 x^{3} - 5 x^{2} + x + 6)

\int cot^{3} (x) csc^{3} (x) d x

\frac{d}{d x} ((x^{3} - 4 x^{2} - 6 x + 1) (x^{2} - 3 x + 1))

\frac{d}{d x} (x (2 x + 3)^{5})

What is (\partial)/(\partial x)(y^{2x}) ?
The answer to (\partial)/(\partial x)(y^{2x}) is 2y^{2x}ln(y)