Solve 6x^{3}-5xy^{2}+3x^{3}-5x^3+2xy^2+3xy^2+2x^3=

$$6 x ^ { 3 } - 5 x y ^ { 2 } + 3 x ^ { 3 } - 5 x ^ { 3 } + 2 x y ^ { 2 } + 3 x y ^ { 2 } + 2 x ^ { 3 } =$$

Evaluate

$$6x^{3}$$

Solution Steps

Combine 3x^{3} and -5x^{3} to get -2x^{3}.

$$6x^{3}-5xy^{2}-2x^{3}+2xy^{2}+3xy^{2}+2x^{3}$$

Combine 2xy^{2} and 3xy^{2} to get 5xy^{2}.

$$6x^{3}-5xy^{2}-2x^{3}+5xy^{2}+2x^{3}$$

Combine -2x^{3} and 2x^{3} to get 0.

$$6x^{3}-5xy^{2}+5xy^{2}$$

Combine -5xy^{2} and 5xy^{2} to get 0.

$$6x^{3}$$

Differentiate w.r.t. x

$$18x^{2}$$

Steps Using Definition of a Derivative

Combine 3x^{3} and -5x^{3} to get -2x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3}-5xy^{2}-2x^{3}+2xy^{2}+3xy^{2}+2x^{3})$$

Combine 2xy^{2} and 3xy^{2} to get 5xy^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3}-5xy^{2}-2x^{3}+5xy^{2}+2x^{3})$$

Combine -2x^{3} and 2x^{3} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3}-5xy^{2}+5xy^{2})$$

Combine -5xy^{2} and 5xy^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3})$$

The derivative of ax^{n} is nax^{n-1}.

$$3\times 6x^{3-1}$$

Multiply 3 times 6.

$$18x^{3-1}$$

Subtract 1 from 3.

$$18x^{2}$$