Find dy/dx in each of the following.
Question 1 :
y = (x2 + 5)3
Question 2 :
y = e2x
Question 3 :
Question 4 :
y = ln(1 + x2)
Question 5 :
1. Answer :
y = (x2 + 5)3
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.
2. Answer :
y = e2x
Let u = 2x.
Then, y = eu.
Now, y is a function of u and u is a function of x.
Chain Rule of Derivative :
On the right side, substitute y = eu and u = e2x and find the derivatives.
3. Answer :
Let u = x3 + 3x2 + 5.
Then, y = eu.
Now, y is a function of u and u is a function of x.
Chain Rule of Derivative :
On the right side, substitute y = eu and u = x3 + 3x2 + 5 and find the derivatives.
4. Answer :
y = ln(1 + x2)
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.
5. Answer :
Let u = x2 - 2x + 13.
Then, y = √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 = √u and u = x2 - 2x + 13 and find the derivatives.
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