Calculus Examples

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

Step 1

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

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

Step 2

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

$0 + \frac{d}{d y} [- 5 x^{2}] + \frac{d}{d y} [x] + \frac{d}{d y} [6]$

Step 3

Since $- 5 x^{2}$ is constant with respect to $y$ , the derivative of $- 5 x^{2}$ with respect to $y$ is $0$ .

$0 + 0 + \frac{d}{d y} [x] + \frac{d}{d y} [6]$

Step 4

Since $x$ is constant with respect to $y$ , the derivative of $x$ with respect to $y$ is $0$ .

$0 + 0 + 0 + \frac{d}{d y} [6]$

Step 5

Since $6$ is constant with respect to $y$ , the derivative of $6$ with respect to $y$ is $0$ .

$0 + 0 + 0 + 0$

Step 6

Combine terms.

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Step 6.1

Add $0$ and $0$ .

$0 + 0 + 0$

Step 6.2

Add $0$ and $0$ .

$0 + 0$

Step 6.3

Add $0$ and $0$ .

$0$