What is (\partial)/(\partial x)(5^{xy}) ?

The answer to (\partial)/(\partial x)(5^{xy}) is ln(5)*5^{xy}y

(\partial)/(\partial x)(5^{xy})

\frac{\partial}{\partial x} (5^{x y})

ln (5) \cdot 5^{x y} y

Solution steps

\frac{\partial}{\partial x} (5^{x y})

Treat

y

as a constant

Apply exponent rule:

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

5^{x y} = e^{x y l n (5)}

= \frac{\partial}{\partial x} (e^{x y l n (5)})

Apply the chain rule:

e^{x y l n (5)} \frac{\partial}{\partial x} (x y ln (5))

= e^{x y l n (5)} \frac{\partial}{\partial x} (x y ln (5))

\frac{\partial}{\partial x} (x y ln (5)) = ln (5) y

= e^{x y l n (5)} ln (5) y

e^{x y l n (5)} = 5^{x y}

= ln (5) \cdot 5^{x y} y

x \to 0 lim (x^{2} sin (\frac{3}{x}))

\frac{\partial}{\partial x} (ln (x - 2 y) - z)

\int_{- 7}^{7} (6 - ∣ x ∣) d x

\int (\frac{3}{2} x + 5)^{\frac{1}{3}} d x

\int x^{2} e^{- 2 x} + 5 e^{- 2 x} d x

What is (\partial)/(\partial x)(5^{xy}) ?
The answer to (\partial)/(\partial x)(5^{xy}) is ln(5)*5^{xy}y