Question

If y= 3√x5 -find dy/dx​

Answer 1

Answer:

−

3

According Leibniz integral rule-

dx

d

∫

a(x)

b(x)

f(x)dx

=f(b(x))

dx

d

b(x)−f(a(x))

dx

d

a(x)

So,

dx

dy

=

dx

dx

2

5−(x

2

)

2

−

dx

dx

5−x

2

⟹

dx

dy

=2x

5−x

4

−

5−x

2

At x=

2

,⟹

dx

dy

=2

2

5−4

−

5−2

dx

dy

=2

2

−

3