Solve =d/dy(10x^3y^5+y)

$$= \frac { d } { d y } ( 10 x ^ { 3 } y ^ { 5 } + y )$$

Evaluate

$$50x^{3}y^{4}+1$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$y^{1-1}+5\times 10x^{3}y^{5-1}$$

Subtract 1 from 1.

$$y^{0}+5\times 10x^{3}y^{5-1}$$

Multiply 5 times 10x^{3}.

$$y^{0}+50x^{3}y^{5-1}$$

Subtract 1 from 5.

$$y^{0}+50x^{3}y^{4}$$

For any term t except 0, t^{0}=1.

$$1+50x^{3}y^{4}$$

Differentiate w.r.t. x

$$150x^{2}y^{4}$$