Math Problem Statement

Solve for the derivatives of the following functions.

Solution

The image you provided contains several differentiation problems. I'll walk through the first one and guide you through the solution:

  1. y = 5

    The derivative of a constant is always zero. Since there is no variable involved, the derivative of 5 is:

    ddx(5)=0\frac{d}{dx}(5) = 0

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Math Problem Analysis

Mathematical Concepts

Differentiation
Derivatives
Power Rule
Product Rule

Formulas

d/dx [c] = 0 (Derivative of a constant)
d/dx [x^n] = n*x^(n-1) (Power Rule)
d/dx [f(x) * g(x)] = f'(x)g(x) + f(x)g'(x) (Product Rule)
d/dx [√x] = (1/2)x^(-1/2)

Theorems

Fundamental Theorem of Calculus
Power Rule of Differentiation

Suitable Grade Level

Grades 10-12

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