What is the derivative of x^{8y} ?

The derivative of x^{8y} is 8x^{8y}(ln(x)(dy)/(dx)+y/x)

What is the first derivative of x^{8y} ?

The first derivative of x^{8y} is 8x^{8y}(ln(x)(dy)/(dx)+y/x)

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\frac{d}{d x} (x^{8 y})

8 x^{8 y} (ln (x) \frac{d y}{d x} + \frac{y}{x})

Solution steps

\frac{d}{d x} (x^{8 y})

Apply exponent rule:

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

x^{8 y} = e^{8 y l n (x)}

= \frac{d}{d x} (e^{8 y l n (x)})

Apply the chain rule:

e^{8 y l n (x)} \frac{d}{d x} (8 y ln (x))

= e^{8 y l n (x)} \frac{d}{d x} (8 y ln (x))

\frac{d}{d x} (8 y ln (x)) = 8 (ln (x) \frac{d y}{d x} + \frac{y}{x})

= e^{8 y l n (x)} \cdot 8 (ln (x) \frac{d y}{d x} + \frac{y}{x})

e^{8 y l n (x)} = x^{8 y}

= 8 x^{8 y} (ln (x) \frac{d y}{d x} + \frac{y}{x})

y = arcsin (2 x), x = \frac{3}{4}

y^{^{'}} = (y + 5) (x + 2)

\int_{0}^{1} \frac{18}{4 y - 1} d y

f (x) = \frac{7}{x}, at x = 4

f (x) = ln (cos^{2} (x))

What is the derivative of x^{8y} ?
The derivative of x^{8y} is 8x^{8y}(ln(x)(dy)/(dx)+y/x)
What is the first derivative of x^{8y} ?
The first derivative of x^{8y} is 8x^{8y}(ln(x)(dy)/(dx)+y/x)