Find the Derivative - d/dx 6x^2+5xy-3z^2

$6 x^{2} + 5 x y - 3 z^{2}$

Step 1

By the Sum Rule, the derivative of $6 x^{2} + 5 x y - 3 z^{2}$ with respect to $x$ is $\frac{d}{d x} [6 x^{2}] + \frac{d}{d x} [5 x y] + \frac{d}{d x} [- 3 z^{2}]$ .

$\frac{d}{d x} [6 x^{2}] + \frac{d}{d x} [5 x y] + \frac{d}{d x} [- 3 z^{2}]$

Step 2

Evaluate $\frac{d}{d x} [6 x^{2}]$ .

Since $6$ is constant with respect to $x$ , the derivative of $6 x^{2}$ with respect to $x$ is $6 \frac{d}{d x} [x^{2}]$ .

$6 \frac{d}{d x} [x^{2}] + \frac{d}{d x} [5 x y] + \frac{d}{d x} [- 3 z^{2}]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 2$ .

$6 (2 x) + \frac{d}{d x} [5 x y] + \frac{d}{d x} [- 3 z^{2}]$

Multiply $2$ by $6$ .

$12 x + \frac{d}{d x} [5 x y] + \frac{d}{d x} [- 3 z^{2}]$

Step 3

Evaluate $\frac{d}{d x} [5 x y]$ .

Since $5 y$ is constant with respect to $x$ , the derivative of $5 x y$ with respect to $x$ is $5 y \frac{d}{d x} [x]$ .

$12 x + 5 y \frac{d}{d x} [x] + \frac{d}{d x} [- 3 z^{2}]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 1$ .

$12 x + 5 y \cdot 1 + \frac{d}{d x} [- 3 z^{2}]$

Multiply $5$ by $1$ .

$12 x + 5 y + \frac{d}{d x} [- 3 z^{2}]$

Step 4

Differentiate using the Constant Rule.

Since $- 3 z^{2}$ is constant with respect to $x$ , the derivative of $- 3 z^{2}$ with respect to $x$ is $0$ .

$12 x + 5 y + 0$

Add $12 x + 5 y$ and $0$ .

$12 x + 5 y$

Find the Derivative - d/dx 6x^2+5xy-3z^2

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