**What is the value of \[\dfrac{d}{dx}\left(\dfrac{1}{x^4}-\dfrac{3}{x^2}\right)\] at \[x=1\]?**

To find the value of the derivative at \( x = 1 \), we need to differentiate the expression \( \dfrac{1}{x^4} - \dfrac{3}{x^2} \) with respect to \( x \), and then substitute \( x = 1 \) into the result.

### Step 1: Differentiate \( \dfrac{1}{x^4} \)

We can rewrite \( \dfrac{1}{x^4} \) as \( x^{-4} \). Now, differentiate it:
\[
\frac{d}{dx} \left( x^{-4} \right) = -4x^{-5}
\]

### Step 2: Differentiate \( -\dfrac{3}{x^2} \)

We can rewrite \( -\dfrac{3}{x^2} \) as \( -3x^{-2} \). Now, differentiate it:
\[
\frac{d}{dx} \left( -3x^{-2} \right) = 6x^{-3}
\]

### Step 3: Combine the derivatives

Now, combine the two derivatives:
\[
\frac{d}{dx} \left( \dfrac{1}{x^4} - \dfrac{3}{x^2} \right) = -4x^{-5} + 6x^{-3}
\]

### Step 4: Substitute \( x = 1 \)

Now, substitute \( x = 1 \) into the derivative:
\[
-4(1)^{-5} + 6(1)^{-3} = -4 +

What is the value of \[\dfrac{d}{dx}\left(\dfrac{1}{x^4}-\dfrac{3}{x^2}\right)\] at \[x=1\]? 

This step-by-step guide explains how to differentiate the expression \(\dfrac{1}{x^4} - \dfrac{3}{x^2}\) using basic calculus principles. Learn how to apply the power rule and substitution to solve this problem, suitable for Grades 11-12 or introductory university calculus.

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