What is the value of (d)/(dx)((1)/(x^(5))) at x=2 ?

Rewrite function as x^(-5): We need to find the derivative of the function f(x) = 1/x^5 with respect to x. To do this, we will use the power rule for derivatives, which states that the derivative of x^n with respect to x is n*x^(n-1). In this case, we can rewrite 1/x^5 as x^(-5).Apply power rule: Now, we apply the power rule to find the derivative of x^(-5). The derivative of x^(-5) with respect to x is -5*x^(-5-1) or -5*x^(-6).Evaluate at x=2: Next, we evaluate the derivative at x=2. So, we substitute x with 2 in the expression -5*x^(-6). This gives us -5*2^(-6).Calculate 2^(-6): We calculate 2^(-6) which is 1/2^6. 2^6 is 64, so 2^(-6) is 1/64.Multiply by -5: Now, we multiply -5 by 1/64. This gives us -5/64.Final result: Therefore, the value of the derivative of (1/x^5) at x=2 is -5/64.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What is the value of
(d)/(dx)((1)/(x^(5))) at
x=2 ?

What is the value of $\frac{d}{d x}\left(\frac{1}{x^{5}}\right)$ at $x=2$ ?

View step-by-step help

Home

Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. What is the value of

\frac{d}{d x}\left(\frac{1}{x^{5}}\right)

x=2

Rewrite function as $x^{-5}$ : We need to find the derivative of the function $f(x) = \frac{1}{x^5}$ with respect to $x$ . To do this, we will use the power rule for derivatives, which states that the derivative of $x^n$ with respect to $x$ is $n \cdot x^{(n-1)}$ . In this case, we can rewrite $\frac{1}{x^5}$ as $x^{-5}$ .
Apply power rule: Now, we apply the power rule to find the derivative of $x^{-5}$ . The derivative of $x^{-5}$ with respect to $x$ is $-5\cdot x^{-5-1}$ or $-5\cdot x^{-6}$ .
Evaluate at $x=2$ : Next, we evaluate the derivative at $x=2$ . So, we substitute $x$ with $2$ in the expression $-5\cdot x^{-6}$ . This gives us $-5\cdot 2^{-6}$ .
Calculate $2^{-6}$ : We calculate $2^{-6}$ which is $1/2^6$ . $2^6$ is $64$ , so $2^{-6}$ is $1/64$ .
Multiply by $-5$ : Now, we multiply $-5$ by $\frac{1}{64}$ . $\newline$ This gives us $-\frac{5}{64}$ .
Final result: Therefore, the value of the derivative of $(\frac{1}{x^5})$ at $x=2$ is $-\frac{5}{64}$ .