Solve (-8+4x^{2}+4xy^2)+(9x^3-x^2+xy^2)

$$( - 8 + 4 x ^ { 2 } + 4 x y ^ { 2 } ) + ( 9 x ^ { 3 } - x ^ { 2 } + x y ^ { 2 } )$$

Differentiate w.r.t. x

$$27x^{2}+6x+5y^{2}$$

Steps Using Derivative Rule for Sum

Combine 4x^{2} and -x^{2} to get 3x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8+3x^{2}+4xy^{2}+9x^{3}+xy^{2})$$

Combine 4xy^{2} and xy^{2} to get 5xy^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8+3x^{2}+5xy^{2}+9x^{3})$$

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}.

$$2\times 3x^{2-1}+5y^{2}x^{1-1}+3\times 9x^{3-1}$$

Multiply 2 times 3.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

Multiply 1 times 5y^{2}.

$$6x^{1}+5y^{2}x^{0}+27x^{3-1}$$

Subtract 1 from 3.

$$6x^{1}+5y^{2}x^{0}+27x^{2}$$

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

$$6x+5y^{2}x^{0}+27x^{2}$$

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

$$6x+5y^{2}\times 1+27x^{2}$$

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

$$6x+5y^{2}+27x^{2}$$

Evaluate

$$9x^{3}+3x^{2}+5xy^{2}-8$$