Mathematics - Calculus - Derivatives
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Apply differentiation rules to find the derivatives of the functions.
Express the derivative dy/dx in terms of x without first rewriting y as a function of x.
1. y=u^5 and u=1/3x-2
Identify a function u of x and an integer such that f(x)=u^n. Then compute f '(x).
1. f(x)= ½+5x^3
2. f(x)=(x^2 - 4x + 1)^3
3.
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The expert examines calculus derivatives. A complete, neat and step-by-step solutions are provided.
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(1) w(z) = z^2 [2z^3 - (3/4)z^-4]
w'(z) = (z^2) [6z^2 - (3/4)(-4)z^-5] + [2z^3 - (3/4)z^-4] (2z)
= 8z^4 - 1.5/z^4 + 3/z^3
(2) dy/dx = dy/du * du/dx = ...
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