Find the Derivative - d/dx (4x-5)^2

Problem

d(4*x−5)/d(x)

Solution

1. Identify the rule needed for the derivative. Since the expression is a function raised to a power, apply the chain rule, which states d(un)/d(x)=n*u(n−1)⋅d(u)/d(x)

2. Apply the power rule to the outer function by bringing the exponent 2 to the front and decreasing the exponent by 1

d(4*x−5)/d(x)=2*(4*x−5)(2−1)⋅d(4*x−5)/d(x)

3. Differentiate the inner function 4*x−5 with respect to x

d(4*x−5)/d(x)=4

4. Substitute the derivative of the inner function back into the expression.

2*(4*x−5)1⋅4

5. Simplify the expression by multiplying the constants 2 and 4

8*(4*x−5)

6. Distribute the constant 8 into the binomial.

32*x−40

Final Answer

d(4*x−5)/d(x)=32*x−40

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