Question

If y = eax than x. dy/dy =​

Answer 1

EXPLANATION.

If y = eᵃˣ.

As we know that,

Taking log on both sides of the equation, we get.

⇒ ㏒(y) = ㏒(eᵃˣ).

Differentiate w.r.t x, we get.

⇒ ㏒(y) = ax.

⇒ 1/y. dy/dx = a.

⇒ dy/dx = a. y.

⇒ dy/dx = a(eᵃˣ).

Multiply both sides of the equation with x, we get.

⇒ x. dy/dx = a(eᵃˣ)(x).

⇒ x. dy/dx = axy.

Option [C] is the correct answer.

                                                                                                                       

MORE INFORMATION.

(1) = d(constant)/dx = 0.

(2) = d(ax)/dx = a.

(3) = d(xⁿ)/dx = nxⁿ⁻¹.

(4) = d(eˣ)/dx = eˣ.

(5) = d(aˣ)/dx = aˣ㏒(a).

(6) = d(㏒ x)/dx = 1/x.

(7) = d(㏒_a x)/dx = 1/x㏒(a).