Solve x^2+(-3x-x^left(2^2right)^2

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

Evaluate

$$x\left(-x^{15}+x-3\right)$$

Solution Steps

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

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

Calculate 2 to the power of 4 and get 16.

$$x^{2}-3x-x^{16}$$

Differentiate w.r.t. x

$$-16x^{15}+2x-3$$

Steps Using Derivative Rule for Sum

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

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

Calculate 2 to the power of 4 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-3x-x^{16})$$

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}.

$$2x^{2-1}-3x^{1-1}+16\left(-1\right)x^{16-1}$$

Subtract 1 from 2.

$$2x^{1}-3x^{1-1}+16\left(-1\right)x^{16-1}$$

Subtract 1 from 1.

$$2x^{1}-3x^{0}+16\left(-1\right)x^{16-1}$$

Multiply 1 times -3.

$$2x^{1}-3x^{0}-16x^{16-1}$$

Subtract 1 from 16.

$$2x^{1}-3x^{0}-16x^{15}$$

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

$$2x-3x^{0}-16x^{15}$$

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

$$2x-3-16x^{15}$$