Question

Derivative of (a^x/Log a)?​

Answer 1

a^x.

Explanation:

y = a^x / log a

Assuming the log is to the base e:

y = (1/ log a) * a^x

Derivative of a^x:

Let u = a^x

log u = log a^x

log u = x log a

1/u * du/dx = log a

du/dx = = u * log a

y = (1 / log a) * u

so dy/du = 1/log a

and dy/dx = dy/du * du/dx

= (1/log a )* log a u

= u

= a^x.

Answer 2

`\large\bold{\underline{\underline{To \: \: Differentive:-}}}`

`\sf{(a^x)/(log(a)) }`

(OR)

`\sf{(a^x)/(ln(a)) }`

`\large\bold{\underline{\underline{Solution:-}}}`

`\sf{Let\ y=(a^x)/(ln(a)) }`

`\sf{=(d)/(dx)\bigg[(a^x)/(ln(a)) \bigg] }`

(Linear differentiation)

`\sf{=(1)/(ln(a)).(d)/(dx)(a^x) }`

`\sf{=(ln(a)a^x)/(ln(a)) }`

`\boxed{\sf{=a^x}}`

`\large\bold{\underline{\underline{Applied:-}}}`

✭ Linear differentiation

→
`\sf{[a.b(x)+c.d(x)]'=a.b'(x)+c.d'(x)}`

✭ Exponential function rule

→
`\sf{(a^x)'=ln(a).a^x}`