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

The derivative of 3^{3-x} is -ln(3)*3^{3-x}

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

The first derivative of 3^{3-x} is -ln(3)*3^{3-x}

derivative of

3^{3 - x}

- ln (3) \cdot 3^{3 - x}

Solution steps

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

Apply exponent rule:

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

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

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

Apply the chain rule:

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

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

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

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

Simplify

e^{(3 - x) l n (3)} (- ln (3)) : - ln (3) \cdot 3^{3 - x}

= - ln (3) \cdot 3^{3 - x}

d er i v a t i v e x^{2} + 5 x - 3

\frac{d}{d x} (i \cdot x \cdot 1 - 2 x)

d er i v a t i v e 4 x^{2} y + 1

\frac{d}{d t} (20 sin (2 t - 3 x))

d er i v a t i v e y = 3 x^{7}

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