Solve x^8y-8xy+3x^6-6

$$x ^ { 8 } y - 8 x y + 3 x ^ { 6 } - 6$$

Differentiate w.r.t. x

$$18x^{5}+8yx^{7}-8y$$

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}.

$$8yx^{8-1}+\left(-8y\right)x^{1-1}+6\times 3x^{6-1}$$

Subtract 1 from 8.

$$8yx^{7}+\left(-8y\right)x^{1-1}+6\times 3x^{6-1}$$

Subtract 1 from 1.

$$8yx^{7}+\left(-8y\right)x^{0}+6\times 3x^{6-1}$$

Multiply 1 times -8y.

$$8yx^{7}+\left(-8y\right)x^{0}+18x^{6-1}$$

Subtract 1 from 6.

$$8yx^{7}+\left(-8y\right)x^{0}+18x^{5}$$

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

$$8yx^{7}+\left(-8y\right)\times 1+18x^{5}$$

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

$$8yx^{7}-8y+18x^{5}$$

Evaluate

$$3x^{6}-8xy+yx^{8}-6$$