Solve 15xy^{5}+7x^2y^3+9x^6y^4-10

$$15 x y ^ { 5 } + 7 x ^ { 2 } y ^ { 3 } + 9 x ^ { 6 } y ^ { 4 } - 10$$

Differentiate w.r.t. x

$$y^{3}\left(14x+15y^{2}+54yx^{5}\right)$$

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}.

$$15y^{5}x^{1-1}+2\times 7y^{3}x^{2-1}+6\times 9y^{4}x^{6-1}$$

Subtract 1 from 1.

$$15y^{5}x^{0}+2\times 7y^{3}x^{2-1}+6\times 9y^{4}x^{6-1}$$

Multiply 2 times 7y^{3}.

$$15y^{5}x^{0}+14y^{3}x^{2-1}+6\times 9y^{4}x^{6-1}$$

Subtract 1 from 2.

$$15y^{5}x^{0}+14y^{3}x^{1}+6\times 9y^{4}x^{6-1}$$

Multiply 2 times 7y^{3}.

$$15y^{5}x^{0}+14y^{3}x^{1}+54y^{4}x^{6-1}$$

Subtract 1 from 6.

$$15y^{5}x^{0}+14y^{3}x^{1}+54y^{4}x^{5}$$

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

$$15y^{5}x^{0}+14y^{3}x+54y^{4}x^{5}$$

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

$$15y^{5}\times 1+14y^{3}x+54y^{4}x^{5}$$

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

$$15y^{5}+14y^{3}x+54y^{4}x^{5}$$

Evaluate

$$7x^{2}y^{3}+15xy^{5}+9y^{4}x^{6}-10$$