Find the derivative of e^ax+b by first principal

ae^ax+b

Step-by-step explanation:

If differentiating something with respect to x, or when finding the derivative on an expression in terms of x

First principal:

f'(x) = lim h → 0, f(x+h)-f(x)/h

f(x+h) = (x+h)^n

f'(x) = lim h → 0, (x+h)^n + x^n / h

Because the power rule states: d/dx[x^n} = nx^n-1.

So, d/dx [e^ax+b] = d/dx[ax+b] × e^ax+b = a × e^ax + b = ae^ax+b

d.) yes, because the volume of the cone is greater than the volume of the sphere

step-by-step explanation:

a, b, c, d are correct.

step-by-step explanation:

we have g(x) = 3 and are required to find which option is a translation of g(x).

now, 'translation' is a transformation which means to shift the function in any direction and the general form of translation is g(x) + k, where k is any real number.

so, according to the options we see that all are correct as they satisfy the general form of translation.

also, it can be seen from the graph below that the function g(x) = 3 is shifted from its position in all the four options.