Find First And Second Partial Differential Coo. Evaluate Lim (x2 + 1) (x-1) / x->2. Determine the nature of the stationary poin.

August 24, 2026Mathematics

ScanSolve AI Answer

August 24, 2026

Answer

$6x^2$

Here's the derivation for question 6.b:

Step 1: Simplify the expression for $Y$ . $Y = X^2 (2x)$ $Y = 2x^{2+1}$ $Y = 2x^3$

Step 2: Differentiate the simplified expression with respect to $x$ . Recall that $\frac{d}{dx}(ax^n) = nax^{n-1}$ . $\frac{dY}{dx} = \frac{d}{dx}(2x^3)$ $\frac{dY}{dx} = 2(3)x^{3-1}$ $\frac{dY}{dx} = 6x^2$

The derivative is: $\boxed{6x^2}$

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Here's the derivation for question 6.b: Step 1: Simplify the expression for Y.
Y = X^2 (2x) Y = 2x^2+1 Y = 2x^3 Step 2: Differentiate the simplified expression with respect to x.
Recall that (d)/(dx)(ax^n) = nax^n-1.

Asked on August 24, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on August 24, 2026

Here's the derivation for question 6.b: Step 1: Simplify the expression for Y. Y = X^2 (2x) Y = 2x^2+1 Y = 2x^3 Step 2: Differentiate the simplified expression with respect to x. Recall that (d)/(dx)(ax^n) = nax^n-1. (dY)/(dx) = (d)/(dx)(2x^3) (dY)/(dx) = 2(3)x^3-1 (dY)/(dx) = 6x^2 The derivative is: 6x^2 Last free one today — make it count tomorrow, or type /upgrade for unlimited.