What is (\partial)/(\partial x)(y^{7x}) ?

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

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(\partial)/(\partial x)(y^{7x})

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

7 y^{7 x} ln (y)

Solution steps

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

Treat

y

as a constant

Apply exponent rule:

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

y^{7 x} = e^{7 x l n (y)}

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

Apply the chain rule:

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

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

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

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

e^{7 x l n (y)} = y^{7 x}

= 7 y^{7 x} ln (y)

y^{^{'}} = \frac{1}{2} y

4^{c o s (3 t)}

sin (t - π)

\int \frac{3 x}{x ^{2} - x - 2} d x

(x - 1) d y + (y - x^{2} + 2 x^{- 3}) d x = 0

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