DERIVATIVE OF A FUNCTION OF FUNCTION

Find the derivative of each function with respect to x.

Problem 1 :

y = (x² + 5x + 6)³

Solution :

y = (x² + 5x + 6)³

Let u = x² + 5x + 6.

Then, we have

y = u³ and u = x² + 5x + 6

Problem 2 :

Solution :

Let u = x³ + 5.

Then, we have

y = e^u and u = x³ + 5

Problem 3 :

Solution :

Let u = x² - 11x + 24.

Then, we have

Problem 4 :

Solution :

Let u = ln x.

Then, we have

Problem 5 :

y = ln (1 + x²)

Solution :

Let u = 1 + x².

Then, we have

y = ln u and u = 1 + x²

Problem 6 :

y = e^{sin x}

Solution :

Let u = sin x.

Then, we have

y = e^u and u = sin x

Problem 7 :

y = ln (tan x)

Solution :

Let u = tan x.

Then, we have

y = ln u and u = tan x

Problem 8 :

y = tan (cos x)

Solution :

Let u = cos x.

Then, we have

y = tan u and u = cos x

Problem 9 :

y = cos (sin 2x)

Solution :

Let u = sin 2x and v = 2x.

Then, we have

y = cos u, u = sin v and v = 2x

Problem 10 :

y = sin (sin x²)

Solution :

Let u = sin x² and v = x².

Then, we have

y = sin u, u = sin v and v = x²

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