What is the derivative of 3^{x-inx} ?

The derivative of 3^{x-inx} is 3^{x-inx}(ln(3)-iln(3)n)

What is the first derivative of 3^{x-inx} ?

The first derivative of 3^{x-inx} is 3^{x-inx}(ln(3)-iln(3)n)

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\frac{d}{d x} (3^{x - in x})

3^{x - in x} (ln (3) - i ln (3) n)

Solution steps

\frac{d}{d x} (3^{x - in x})

Apply exponent rule:

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

3^{x - in x} = e^{(x - in x) l n (3)}

= \frac{d}{d x} (e^{(x - in x) l n (3)})

Apply the chain rule:

e^{(x - in x) l n (3)} \frac{d}{d x} ((x - in x) ln (3))

= e^{(x - in x) l n (3)} \frac{d}{d x} ((x - in x) ln (3))

\frac{d}{d x} ((x - in x) ln (3)) = ln (3) - i ln (3) n

= e^{(x - in x) l n (3)} (ln (3) - i ln (3) n)

e^{(x - in x) l n (3)} = 3^{x - in x}

= 3^{x - in x} (ln (3) - i ln (3) n)

What is the derivative of 3^{x-inx} ?
The derivative of 3^{x-inx} is 3^{x-inx}(ln(3)-iln(3)n)
What is the first derivative of 3^{x-inx} ?
The first derivative of 3^{x-inx} is 3^{x-inx}(ln(3)-iln(3)n)