In several weeks, we will introduce Calculus into our discussion. Starting in th

Question

In several weeks, we will introduce Calculus into our discussion. Starting in this assignment, we ask some computational questions from Calculus. The functions that appear often in Probability are (here x is the function variable) power terms x^d where d is a number. Recall that 1/x^d is the same as x^-d, and that fractional exponents correspond to roots. e^x. Generally, there are many terms e^f(x), where f(x) is a function in x. The generalized version is differentiated using the Chain Rule. In(x) and, more generally, In(f(x)). For this week, differentiate the following functions. 1. 2x^7 2. 3e^-5x 3. 4/x 4. 8In(x) Enter formula using calculator notation. For example, x^2 is ' x^2' and x -e^4x would be " x e^(4x)' or "x"e^(4x)".

Explanation / Answer

Some standard differentials:

Differentiation of: x^a = ax^(a-1)

Differentiation of: e^(kx)=-ke^(x)

Differentiation of: ln(x) = 1/x

1. Differentiation of 2*x^7 = 2*7*x^(7-1) = 14*x^6

2. Differentiation of 3*e^(-5x) = 3*(-5)*e^(-5x) = -15*e^(-5x)

3. 4/x = 4*^(-1)

Differentiation of 4*x^(-1) = -4*x^(-2) = -4/x^(2)

4. Differentiation of 8*ln(x) = 8/x

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