Find the derivatives of the following functions: y = 3 ^ x + 4ln3x

Find the derivative of this function: y = 3 ^ x + 4ln 3x.

Using the formulas:

(a ^ x) ’= a ^ x * ln a (derivative of the basic elementary function).

(ln x) ’= 1 / x (derivative of the basic elementary function).

(c * u) ’= c * u’, where c is const (basic rule of differentiation).

(u + v) ’= u’ + v ’(basic rule of differentiation).

y = f (g (x)), y ’= f’u (u) * g’x (x), where u = g (x) (basic rule of differentiation).

Thus, the derivative of our function will be as follows:

y ‘= (3 ^ x + 4ln 3x)’ = (3 ^ x) ‘+ (4ln 3x)’ = (3 ^ x) ‘+ (3x)’ * (4ln 3x) ‘= 3 ^ x * ln 3 + 3 * 4 * (1 / 3x) = 3 ^ x * ln 3 + 12 / 3x.

Answer: y ‘= 3 ^ x * ln 3 + 12 / 3x.