What is (\partial)/(\partial x)(e^{(7xy)}ln(6y)) ?

The answer to (\partial)/(\partial x)(e^{(7xy)}ln(6y)) is ln(6y)e^{7xy}*7y

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(\partial)/(\partial x)(e^{(7xy)}ln(6y))

\frac{\partial}{\partial x} (e^{(7 x y)} ln (6 y))

ln (6 y) e^{7 x y} \cdot 7 y

Solution steps

\frac{\partial}{\partial x} (e^{(7 x y)} ln (6 y))

Treat

y

as a constant

Take the constant out:

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

= ln (6 y) \frac{\partial}{\partial x} (e^{7 x y})

Apply the chain rule:

e^{7 x y} \frac{\partial}{\partial x} (7 x y)

= e^{7 x y} \frac{\partial}{\partial x} (7 x y)

\frac{\partial}{\partial x} (7 x y) = 7 y

= ln (6 y) e^{7 x y} \cdot 7 y

\int (2 x^{2} - 1) d x

\int 2 cos (x) + 7 d x

\frac{d}{d x} (a x^{2} + b y (x)^{2} + c)

\int_{0}^{y} \int_{0}^{x} (x^{2} + y^{2})^{\frac{3}{2}} d y d x

3 x, \frac{3}{4} x, 70 - x^{2}

What is (\partial)/(\partial x)(e^{(7xy)}ln(6y)) ?
The answer to (\partial)/(\partial x)(e^{(7xy)}ln(6y)) is ln(6y)e^{7xy}*7y