Solve 12+x-left(x^2right)^2

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

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12+x-x^{4})$$

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}.

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

Subtract 1 from 1.

$$x^{0}+4\left(-1\right)x^{4-1}$$

Multiply 4 times -1.

$$x^{0}-4x^{4-1}$$

Subtract 1 from 4.

$$x^{0}-4x^{3}$$

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

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

Evaluate

$$12+x-x^{4}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$12+x-x^{4}$$