Question

difrentiate sec(tanX^3)​

Answer 1

Answer:

3(x^2) × sec[tan(x^3)] tan[tan(x^3)] × sec^2[(x^3)]

Step-by-step explanation:

In questions like this we use the chain rule.

The function here is a composite function, i.e it is made up of more than 1 function.

In this case we have 3 functions together.

FIRST FUNCTION IS sec(p) , where we take p= tan(x^3)

SECOND FUNCTUON IS tan(q) , where q= x^3

THIRD FUNCTION IS x^3

Chain rule says that the Differntiation of the given function is:

d/dx[ sec(p) ] × d/dx [ tan(q) ] × d/dx (x^3)

= sec(p)•tan(p) × sec^2(q) × 3(x^2)

= 3(x^2) × sec[tan(x^3)] tan[tan(x^3)] × sec^2 [(x^3)]

☆ What we did here was differentiate each function seperately and multiply their results.In the end we replaced the values of p and q.

THIS IS THE ANSWER