Find the Derivative - d/dx y=16-x^4

Problem

d()/d(x)*(16−x^4)

Solution

1. Identify the expression to be differentiated, which is a difference of two terms: 16 and x^4

2. Apply the sum/difference rule, which states that the derivative of a sum or difference is the sum or difference of the derivatives.

d()/d(x)*(16−x^4)=d(16)/d(x)−d(x^4)/d(x)

3. Apply the constant rule to the first term. The derivative of any constant, such as 16 is 0

d(16)/d(x)=0

4. Apply the power rule to the second term. For any term x^n the derivative is n*x^(n−1)

d(x^4)/d(x)=4*x^3

5. Combine the results to find the final derivative.

0−4*x^3=−4*x^3

Final Answer

d()/d(x)*(16−x^4)=−4*x^3

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