Solve (3x^4-2x^2-2)+(-2x^4+5)

$$( 3 x ^ { 4 } - 2 x ^ { 2 } - 2 ) + ( - 2 x ^ { 4 } + 5 )$$

Evaluate

$$x^{4}-2x^{2}+3$$

Solution Steps

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

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

Add -2 and 5 to get 3.

$$x^{4}-2x^{2}+3$$

Differentiate w.r.t. x

$$4x\left(x^{2}-1\right)$$

Steps Using Derivative Rule for Sum

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

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

Add -2 and 5 to get 3.

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

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}.

$$4x^{4-1}+2\left(-2\right)x^{2-1}$$

Subtract 1 from 4.

$$4x^{3}+2\left(-2\right)x^{2-1}$$

Multiply 2 times -2.

$$4x^{3}-4x^{2-1}$$

Subtract 1 from 2.

$$4x^{3}-4x^{1}$$

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

$$4x^{3}-4x$$