Algebra Examples

$\frac{d^{2}}{d x^{2}} (\sin (x) + \cos (x))$

Step 1

Cancel the common factor of $d^{2}$ and $d$ .

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Step 1.1

Factor $d$ out of $d^{2}$ .

$\frac{d \cdot d}{d x^{2}} \cdot (\sin (x) + \cos (x))$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $d$ out of $d x^{2}$ .

$\frac{d \cdot d}{d (x^{2})} \cdot (\sin (x) + \cos (x))$

Step 1.2.2

Cancel the common factor.

$\frac{d \cdot d}{d x^{2}} \cdot (\sin (x) + \cos (x))$

Step 1.2.3

Rewrite the expression.

$\frac{d}{x^{2}} \cdot (\sin (x) + \cos (x))$

Step 2

Apply the distributive property.

$\frac{d}{x^{2}} \sin (x) + \frac{d}{x^{2}} \cos (x)$

Step 3

Combine $\frac{d}{x^{2}}$ and $\sin (x)$ .

$\frac{d \sin (x)}{x^{2}} + \frac{d}{x^{2}} \cos (x)$

Step 4

Combine $\frac{d}{x^{2}}$ and $\cos (x)$ .

$\frac{d \sin (x)}{x^{2}} + \frac{d \cos (x)}{x^{2}}$