Find the Derivative - d/dy 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 $y$ is $\frac{d}{d y} [2 x^{8} y^{4}] + \frac{d}{d y} [7 x^{5} y^{4}]$ .

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

Step 2

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

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

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

Differentiate using the Power Rule which states that $\frac{d}{d y} [y^{n}]$ is $n y^{n - 1}$ where $n = 4$ .

$2 x^{8} (4 y^{3}) + \frac{d}{d y} [7 x^{5} y^{4}]$

Multiply $4$ by $2$ .

$8 x^{8} y^{3} + \frac{d}{d y} [7 x^{5} y^{4}]$

Step 3

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

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

$8 x^{8} y^{3} + 7 x^{5} \frac{d}{d y} [y^{4}]$

Differentiate using the Power Rule which states that $\frac{d}{d y} [y^{n}]$ is $n y^{n - 1}$ where $n = 4$ .

$8 x^{8} y^{3} + 7 x^{5} (4 y^{3})$

Multiply $4$ by $7$ .

$8 x^{8} y^{3} + 28 x^{5} y^{3}$

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

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