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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

\frac{d}{d x} (e^{x^{2}} sin (x^{3} - 2))

\frac{d}{d x} (x (x + 1))

\frac{d}{d x} (8^{x - 5})

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

y^{^{''}} + 25 y = 30 sin (5 t)

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