Solve x^5y-9xy+9x^4-8

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

Differentiate w.r.t. x

$$36x^{3}+5yx^{4}-9y$$

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}.

$$5yx^{5-1}+\left(-9y\right)x^{1-1}+4\times 9x^{4-1}$$

Subtract 1 from 5.

$$5yx^{4}+\left(-9y\right)x^{1-1}+4\times 9x^{4-1}$$

Subtract 1 from 1.

$$5yx^{4}+\left(-9y\right)x^{0}+4\times 9x^{4-1}$$

Multiply 1 times -9y.

$$5yx^{4}+\left(-9y\right)x^{0}+36x^{4-1}$$

Subtract 1 from 4.

$$5yx^{4}+\left(-9y\right)x^{0}+36x^{3}$$

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

$$5yx^{4}+\left(-9y\right)\times 1+36x^{3}$$

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

$$5yx^{4}-9y+36x^{3}$$

Evaluate

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