The slope of the tangent line to y 3x at x 0 is A 3 B e C

Solution

The slope of the tangent line is the derivative. Since the function y is an explicit function of x (y=f(x)), you need to evaluate the derivative at x=0. To take the derivative of a power, you take the natural log of the base, multiply it by the original function, and then take the derivative of the exponent (in this case with respect to itself, which equals 1). So you have: d/dx (f(x))= ln(3)*(3^x)*(1)= ln(3)*(3^x). Evaluate @x=0 and you get: = ln(3)*(3^0)= ln(3)*(1)= ln(3), your final answer, choice (D)