What is the derivative of 8^{x-5} ?

The derivative of 8^{x-5} is 3ln(2)*8^{x-5}

What is the first derivative of 8^{x-5} ?

The first derivative of 8^{x-5} is 3ln(2)*8^{x-5}

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\frac{d}{d x} (8^{x - 5})

3 ln (2) \cdot 8^{x - 5}

Solution steps

\frac{d}{d x} (8^{x - 5})

Apply exponent rule:

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

8^{x - 5} = e^{(x - 5) l n (8)}

= \frac{d}{d x} (e^{(x - 5) l n (8)})

Apply the chain rule:

e^{(x - 5) l n (8)} \frac{d}{d x} ((x - 5) ln (8))

= e^{(x - 5) l n (8)} \frac{d}{d x} ((x - 5) ln (8))

\frac{d}{d x} ((x - 5) ln (8)) = 3 ln (2)

= e^{(x - 5) l n (8)} \cdot 3 ln (2)

e^{(x - 5) l n (8)} = 8^{x - 5}

= 3 ln (2) \cdot 8^{x - 5}

\frac{d}{d x} (x (x^{2} - 1)^{2})

y^{^{''}} + 25 y = 30 sin (5 t)

x \to 0 lim (x^{2})

\frac{d}{d x} (ln (x + x^{2} - 12))

3 e^{x}, 3 x e^{x^{2}}, 0, 1

What is the derivative of 8^{x-5} ?
The derivative of 8^{x-5} is 3ln(2)*8^{x-5}
What is the first derivative of 8^{x-5} ?
The first derivative of 8^{x-5} is 3ln(2)*8^{x-5}