CHAIN RULE OF DERIVATIVE

Find dy/dx in each of the following.

Example 1 :

y = (x² + 5)³

Solution :

Let u = x² + 5.

Then, y = u³.

Now, y is a function of u and u is a function of x.

Chain Rule of Derivative :

On the right side, substitute y = u³ and u = x² + 5 and find the derivatives.

Example 2 :

y = e^2x

Solution :

Let u = 2x.

Then, y = e^u.

Now, y is a function of u and u is a function of x.

Chain Rule of Derivative :

On the right side, substitute y = e^u and u = e^2x and find the derivatives.

Example 3 :

Solution :

Let u = x³ + 3x² + 5.

Then, y = e^u.

Now, y is a function of u and u is a function of x.

Chain Rule of Derivative :

On the right side, substitute y = e^u and u = x³ + 3x² + 5  and find the derivatives.

Example 4 :

y = ln(1 + x²)

Solution :

Let u = 1 + x².

Then, y = lnu.

Now, y is a function of u and u is a function of x.

Chain Rule of Derivative :

On the right side, substitute y = lnu and u = 1 + x² and find the derivatives.

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