Find the Derivative - d/dx y=3^xx^3

Problem

d()/d(x)*3*x3

Solution

1. Identify the rule needed for the derivative. Since the expression is a product of two functions, 3 and x3 apply the product rule: (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

2. Differentiate the first part of the product. The derivative of the exponential function 3 is 3*ln(3)

3. Differentiate the second part of the product. Using the power rule, the derivative of x3 is 3*x2

4. Apply the product rule formula by substituting the functions and their derivatives.

(d(3)*x3)/d(x)=3d(x3)/d(x)+x3d(3)/d(x)

5. Substitute the calculated derivatives into the expression.

(d(3)*x3)/d(x)=3*(3*x2)+x3*(3*ln(3))

6. Factor out the common terms 3 and x2 to simplify the final expression.

(d(3)*x3)/d(x)=3*x2*(3+x*ln(3))

Final Answer

(d(3)*x3)/d(x)=3*x2*(3+x*ln(3))

Want more problems? Check here!