Derivative of x^3 + y^5 with respect to y

The calculator will find the derivative of

x^{3} + y^{5}

with respect to

y

, with steps shown.

Find $\frac{d}{dy} \left(x^{3} + y^{5}\right)$ .

The derivative of a sum/difference is the sum/difference of derivatives:

{\color{red}\left(\frac{d}{dy} \left(x^{3} + y^{5}\right)\right)} = {\color{red}\left(\frac{d}{dy} \left(x^{3}\right) + \frac{d}{dy} \left(y^{5}\right)\right)}

Apply the power rule $\frac{d}{dy} \left(y^{n}\right) = n y^{n - 1}$ with $n = 5$ :

{\color{red}\left(\frac{d}{dy} \left(y^{5}\right)\right)} + \frac{d}{dy} \left(x^{3}\right) = {\color{red}\left(5 y^{4}\right)} + \frac{d}{dy} \left(x^{3}\right)

The derivative of a constant is $0$ :

5 y^{4} + {\color{red}\left(\frac{d}{dy} \left(x^{3}\right)\right)} = 5 y^{4} + {\color{red}\left(0\right)}

Thus, $\frac{d}{dy} \left(x^{3} + y^{5}\right) = 5 y^{4}$ .

$\frac{d}{dy} \left(x^{3} + y^{5}\right) = 5 y^{4}$ A

Derivative of x3+y5x^{3} + y^{5}x3+y5 with respect to yyy