Solve (7x^{2}-5a^{2})+(7a^2-5x^2)+(4x^2-2a^2)=

$$( 7 x ^ { 2 } - 5 a ^ { 2 } ) + ( 7 a ^ { 2 } - 5 x ^ { 2 } ) + ( 4 x ^ { 2 } - 2 a ^ { 2 } ) =$$

Evaluate

$$6x^{2}$$

Solution Steps

Combine -5a^{2} and 7a^{2} to get 2a^{2}.

$$7x^{2}+2a^{2}-5x^{2}+4x^{2}-2a^{2}$$

Combine 7x^{2} and -5x^{2} to get 2x^{2}.

$$2x^{2}+2a^{2}+4x^{2}-2a^{2}$$

Combine 2x^{2} and 4x^{2} to get 6x^{2}.

$$6x^{2}+2a^{2}-2a^{2}$$

Combine 2a^{2} and -2a^{2} to get 0.

$$6x^{2}$$

Differentiate w.r.t. x

$$12x$$

Steps Using Definition of a Derivative

Combine -5a^{2} and 7a^{2} to get 2a^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{2}+2a^{2}-5x^{2}+4x^{2}-2a^{2})$$

Combine 7x^{2} and -5x^{2} to get 2x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+2a^{2}+4x^{2}-2a^{2})$$

Combine 2x^{2} and 4x^{2} to get 6x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2}+2a^{2}-2a^{2})$$

Combine 2a^{2} and -2a^{2} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2})$$

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

$$2\times 6x^{2-1}$$

Multiply 2 times 6.

$$12x^{2-1}$$

Subtract 1 from 2.

$$12x^{1}$$

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

$$12x$$