Solve 4x^5y+9xy+8

$$4 x ^ { 5 } y + 9 x y + 8$$

Differentiate w.r.t. x

$$y\left(20x^{4}+9\right)$$

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}.

$$5\times 4yx^{5-1}+9yx^{1-1}$$

Multiply 5 times 4y.

$$20yx^{5-1}+9yx^{1-1}$$

Subtract 1 from 5.

$$20yx^{4}+9yx^{1-1}$$

Subtract 1 from 1.

$$20yx^{4}+9yx^{0}$$

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

$$20yx^{4}+9y\times 1$$

For any term t, t\times 1=t and 1t=t.

$$20yx^{4}+9y$$

Evaluate

$$9xy+4yx^{5}+8$$