Q5.Find the first and second derivatives of the following functions with respect to the given variable: i. f(x) — 2е-2х ii. g(t) = (1 – t²)³ | и iii. h(u) 2и+1

Q: У y = |1 - х - 1+х

A:

Q: Find the derivative of the following function. 3 f(w) = 9w° + 6w + 7w

A: Given,          f(w)=9w5 + 6w3 +7w

Q: Evaluate the first derivative of the function below at (1, -2). 3x4y² - 7xy³ = 4 - 8y

A:

Q: 2t –8 Find the derivative of with respect to t. 4t+8 3t а. (4t+8)² 3t b. (4t+8)? 3 C. (t+2)? 3. d.…

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: