Solve 4-x^4+4x^4-x^2

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

Differentiate w.r.t. x

$$12x^{3}-2x$$

Steps Using Derivative Rule for Sum

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

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

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}.

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

Multiply 4 times 3.

$$12x^{4-1}+2\left(-1\right)x^{2-1}$$

Subtract 1 from 4.

$$12x^{3}+2\left(-1\right)x^{2-1}$$

Multiply 2 times -1.

$$12x^{3}-2x^{2-1}$$

Subtract 1 from 2.

$$12x^{3}-2x^{1}$$

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

$$12x^{3}-2x$$

Evaluate

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

Solution Steps

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

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