What is the derivative of y^x ?

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

What is the first derivative of y^x ?

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

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Popular >

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

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

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

e^{- 0.72}

e^{- 0.62}

e^{- 0.48}

e^{- 0.26}

e^{- 0.22}

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