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Popular >

derivative of e^{yln(x})

Solution

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

Solution

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

Solution steps

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

Simplify

e^{y l n (x)} : x^{y}

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

Popular Examples

simplify 0.4x10^{-3}simplify

0.4 x 1 0^{- 3}

simplify (30*2^t)*(8*1.5^t)simplify

(30 \cdot 2^{t}) \cdot (8 \cdot 1. 5^{t})

simplify 2(2.8*10^{-6})simplify

2 (2.8 \cdot 1 0^{- 6})

simplify (9.32*10^3)(3.32*10^2)simplify

(9.32 \cdot 1 0^{3}) (3.32 \cdot 1 0^{2})

simplify 4.14*10^5(20*10^{-6})simplify

4.14 \cdot 1 0^{5} (20 \cdot 1 0^{- 6})

Frequently Asked Questions (FAQ)

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