Let y = f(u) and u = g(x).
Then the derivative of y with respect to x is
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 = eu 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 = esin x
Solution :
Let u = sin x.
Then, we have
y = eu 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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