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Popular >

derivative of x^r

Solution

\frac{d}{d x} (x^{r})

Solution

x^{r} (ln (x) \frac{d r}{d x} + \frac{r}{x})

Solution steps

\frac{d}{d x} (x^{r})

Apply exponent rule:

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

x^{r} = e^{r l n (x)}

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

Apply the chain rule:

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

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

\frac{d}{d x} (r ln (x)) = ln (x) \frac{d r}{d x} + \frac{r}{x}

= e^{r l n (x)} (ln (x) \frac{d r}{d x} + \frac{r}{x})

e^{r l n (x)} = x^{r}

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

Popular Examples

derivative of e^{x^2-y^2}sin(2xy)

\frac{d}{d x} (e^{x^{2} - y^{2}} sin (2 x y))

integral of cos(1-x)

\int cos (1 - x) d x

simplify 2cos(x^3)-2/x simplify

2 cos (x^{3}) - \frac{2}{x}

normal of y=4x-1,(1,-4)normal of

y = 4 x - 1, (1, - 4)

(\partial)/(\partial x)(4xsin(xy))

\frac{\partial}{\partial x} (4 x sin (x y))

Frequently Asked Questions (FAQ)

What is the derivative of x^r ?
The derivative of x^r is x^r(ln(x)(dr)/(dx)+r/x)
What is the first derivative of x^r ?
The first derivative of x^r is x^r(ln(x)(dr)/(dx)+r/x)