Find derivative of function with fractional exponent?

In summary, the derivative of the function R(t)=5t-3/5 is -3/t^8/5, which can be obtained using the general rule for derivatives of functions with fractional exponents.
  • #1
coolbeans33
23
0
I need to find the derivative of R(t)=5t-3/5

are there any derivative rules I can use for this problem?
 
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  • #2
Re: find derivative of function with fractional exponent?

Welcome to MHB, coolbeans33! :)

coolbeans33 said:
I need to find the derivative of R(t)=5t-3/5

are there any derivative rules I can use for this problem?

Just the regular ones should do.
I presume you know that the derivative of $x^n$ is $nx^{n-1}$?
This is also true if n is a real number.
Or put otherwise: the derivative of $t^\alpha$ is $\alpha t^{\alpha - 1}$ for any real number $\alpha$.
 
  • #3
Re: find derivative of function with fractional exponent?

so the answer is -3t-1.6?
 
Last edited:
  • #4
Re: find derivative of function with fractional exponent?

coolbeans33 said:
so the answer is -3t-1.6?

Yes, although I would only use decimal notation if the exponent is given using such notation. In this case I would write:

\(\displaystyle \frac{d}{dt}\left(5t^{-\frac{3}{5}} \right)=5 \left(- \frac{3}{5} \right)t^{-\frac{3}{5}-1}=-3t^{-\frac{8}{5}}\)
 

FAQ: Find derivative of function with fractional exponent?

1) How do I find the derivative of a function with a fractional exponent?

To find the derivative of a function with a fractional exponent, you can use the power rule. This rule states that for a function f(x) = x^(a/b), the derivative is (a/b)x^(a/b-1). You can also rewrite the function as a rational exponent and then use the chain rule to find the derivative.

2) What is the power rule?

The power rule is a derivative rule that states that for a function f(x) = x^n, the derivative is nx^(n-1). This rule can also be extended to functions with fractional exponents, as stated in the previous answer.

3) Can I use the power rule for any function with a fractional exponent?

No, the power rule can only be used for functions with a single variable raised to a constant fractional exponent. If the exponent contains variables, you may need to use the chain rule or other derivative rules.

4) Are there any other rules for finding derivatives of functions with fractional exponents?

Yes, in addition to the power rule, you can also use the quotient rule or logarithmic differentiation to find derivatives of functions with fractional exponents. Which rule you use will depend on the specific function and its exponent.

5) Is there a specific process for finding the derivative of a function with a fractional exponent?

Yes, when finding the derivative of a function with a fractional exponent, you should first rewrite the function using the rules of exponents. Then, you can use the appropriate derivative rule (power rule, quotient rule, etc.) to find the derivative. Finally, simplify the result if possible.

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