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Popular >

derivative of 2^{xy}

Solution

\frac{d}{d x} (2^{x y})

Solution

ln (2) \cdot 2^{x y} (y + x \frac{d y}{d x})

Solution steps

\frac{d}{d x} (2^{x y})

Apply exponent rule:

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

2^{x y} = e^{x y l n (2)}

= \frac{d}{d x} (e^{x y l n (2)})

Apply the chain rule:

e^{x y l n (2)} \frac{d}{d x} (x y ln (2))

= e^{x y l n (2)} \frac{d}{d x} (x y ln (2))

\frac{d}{d x} (x y ln (2)) = ln (2) (y + x \frac{d y}{d x})

= e^{x y l n (2)} ln (2) (y + x \frac{d y}{d x})

e^{x y l n (2)} = 2^{x y}

= ln (2) \cdot 2^{x y} (y + x \frac{d y}{d x})

Popular Examples

tangent of e^{-3x}tangent of

e^{- 3 x}

derivative of sqrt(tan(\sqrt{x)})

\frac{d}{d x} (tan (x))

limit as x approaches-infinity of 1

x \to - \infty lim (1)

(dy)/(dt)=y(5-ty)

\frac{d y}{d t} = y (5 - t y)

limit as x approaches 8 of ((sqrt(x)-2))/(x-8)

x \to 8 lim (\frac{( x - 2 )}{x - 8})

Frequently Asked Questions (FAQ)

What is the derivative of 2^{xy} ?
The derivative of 2^{xy} is ln(2)*2^{xy}(y+x(dy)/(dx))
What is the first derivative of 2^{xy} ?
The first derivative of 2^{xy} is ln(2)*2^{xy}(y+x(dy)/(dx))