Differentiation

2.4 Find the Derivatives of a Quotient using Quotient Rule Method 1 The Quotient Rule Example: Method 2 (Differentiate Directly) Example: Given that  y = x 2 2 x + 1 ,  find  d y d x Solution: y = x 2 2 x + 1 d y d x = ( 2 x + 1 … Read more

2.3 Find the Derivatives of a Product using Product Rule (A) The Product Rule Method 1 If u(x) and v(x) are two functions of x and y = uv then Example: Method 2 (Differentiate Directly) Example: Given that  y = ( 2 x + 3 ) ( 3 x 3 − 2 x 2 − x … Read more

2.2 First Derivative for Polynomial Function (A) Differentiating a Constant (B) Differentiating Variable with Index n (C) Differentiating a Linear Function (D) Differentiating a Polynomial Function (E) Differentiating Fractional Function (F) Differentiating Square Root Function Example: Find d y d x for each of the following functions: (a) y= 12 (b) y= x4 (c) y= 3x (d) y= 5×3 … Read more

Question 22: Given that   y = 3 4 x 2 , find the approximate change in x which will cause y to decrease from 48 to 47.7. Solution: y = 3 4 x 2 d y d x = ( 2 ) 3 4 x = 3 2 x δ y = 47.7 − … Read more