Derivative of 5
Answer
Derivative of 5
- Rule Used
- Constant Rule
- Steps
- 5 does not depend on x. The slope of a horizontal line is zero, so the constant rule gives 0. A symbol such as pi is still a constant.
- Final answer: 0
d/dx 5 = 0. The expression is built from polynomials, sine, cosine, or exponentials, so the derivative exists for every real x.
Instant step-by-step solution for 5
Derivative of 5 = 0 Solve step-by-step for free: https://derivativecalculatorai.com/derivative-of-constant
Derivative
5 → 0engine: 0
Graph of the function and its derivative
The solid curve is f. The dashed curve is f′. Vertical gaps are asymptotes or jumps, not extra zeros.
Why the derivative has this form
The constant function 5 is a horizontal line. Moving x does not change the output, so the rate of change is 0. This is the prototype for every later constant term: x^2+1, x+1, and pi all lose their constant piece for the same reason.
Apply the power rule to 5. The form to remember, already simplified, is 0.
The expression is built from polynomials, sine, cosine, or exponentials, so the derivative exists for every real x.
At x = 7, substitute into the simplified form 0. That number is the slope of 5 there; a secant over a small step in x lands next to it.
Worked derivative
- Write f(x) = 5.
- Apply the power rule to 5. The form to remember, already simplified, is 0.
- At x = 7, substitute into the simplified form 0. That number is the slope of 5 there; a secant over a small step in x lands next to it.
Common mistakes
Answering 5
Answering 5 confuses the height of the line with its slope. Height can be 5 while the slope stays 0.
Treating 5 as a variable
A symbol in the input is a variable only if it is x. Anything else that does not change with x has slope 0.
Related rule and examples
- Power rule — The rule page lists this example and the others in the same family.
- Derivative of pi — Same family of differentiation, different function.
Frequently asked questions
What is the derivative of 5?
0. The constant function 5 is a horizontal line. Moving x does not change the output, so the rate of change is 0. This is the prototype for every later constant term: x^2+1, x+1, and pi all lose their constant piece for the same reason.
Which wrong answer shows up for 5?
Answering 5 confuses the height of the line with its slope. Height can be 5 while the slope stays 0.
Where is the derivative of 5 defined?
The expression is built from polynomials, sine, cosine, or exponentials, so the derivative exists for every real x.