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Popular >

derivative of x^y+y^x

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Popular Examples

tangent of f(x)=x^3-3x+2,\at x=3 tangent of

f (x) = x^{3} - 3 x + 2, at x = 3

sum from n=1 to infinity of 7(1/10)^n

n = 1 \sum \infty 7 (\frac{1}{10})^{n}

derivative of sin(sqrt(1-x))

\frac{d}{d x} (sin (1 - x))

inverse oflaplace 1/((s+5)^2)inverse laplace

\frac{1}{( s + 5 ) ^{2}}

derivative of (2x^5+3x^4-x^3+2/(x^2))

\frac{d}{d x} (\frac{2 x ^{5} + 3 x ^{4} - x ^{3} + 2}{x ^{2}})

Frequently Asked Questions (FAQ)

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