Find the Derivative - d/dx 2x^8y^4+7x^5y^4

$2 x^{8} y^{4} + 7 x^{5} y^{4}$

Step 1

By the Sum Rule, the derivative of $2 x^{8} y^{4} + 7 x^{5} y^{4}$ with respect to $x$ is $\frac{d}{d x} [2 x^{8} y^{4}] + \frac{d}{d x} [7 x^{5} y^{4}]$ .

$\frac{d}{d x} [2 x^{8} y^{4}] + \frac{d}{d x} [7 x^{5} y^{4}]$

Step 2

Evaluate $\frac{d}{d x} [2 x^{8} y^{4}]$ .

Since $2 y^{4}$ is constant with respect to $x$ , the derivative of $2 x^{8} y^{4}$ with respect to $x$ is $2 y^{4} \frac{d}{d x} [x^{8}]$ .

$2 y^{4} \frac{d}{d x} [x^{8}] + \frac{d}{d x} [7 x^{5} y^{4}]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 8$ .

$2 y^{4} (8 x^{7}) + \frac{d}{d x} [7 x^{5} y^{4}]$

Multiply $8$ by $2$ .

$16 y^{4} x^{7} + \frac{d}{d x} [7 x^{5} y^{4}]$

Step 3

Evaluate $\frac{d}{d x} [7 x^{5} y^{4}]$ .

Since $7 y^{4}$ is constant with respect to $x$ , the derivative of $7 x^{5} y^{4}$ with respect to $x$ is $7 y^{4} \frac{d}{d x} [x^{5}]$ .

$16 y^{4} x^{7} + 7 y^{4} \frac{d}{d x} [x^{5}]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = 5$ .

$16 y^{4} x^{7} + 7 y^{4} (5 x^{4})$

Multiply $5$ by $7$ .

$16 y^{4} x^{7} + 35 y^{4} x^{4}$

Step 4

Reorder terms.

$16 x^{7} y^{4} + 35 x^{4} y^{4}$

Find the Derivative - d/dx 2x^8y^4+7x^5y^4

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