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))

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

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})

(\frac{4}{3})^{4}

1.15 \cdot 1 0^{- 6}

cos (x^{2}) e^{- x}

(e^{- t})^{3}

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))