Solve 2x^4+7^3+x^2-7x-3

$$2 { x }^{ 4 } + { 7 }^{ 3 } + { x }^{ 2 } -7x-3$$

Evaluate

$$2x^{4}+x^{2}-7x+340$$

Solution Steps

Calculate 7 to the power of 3 and get 343.

$$2x^{4}+343+x^{2}-7x-3$$

Subtract 3 from 343 to get 340.

$$2x^{4}+340+x^{2}-7x$$

Differentiate w.r.t. x

$$8x^{3}+2x-7$$

Steps Using Derivative Rule for Sum

Calculate 7 to the power of 3 and get 343.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}+343+x^{2}-7x-3)$$

Subtract 3 from 343 to get 340.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}+340+x^{2}-7x)$$

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}.

$$4\times 2x^{4-1}+2x^{2-1}-7x^{1-1}$$

Multiply 4 times 2.

$$8x^{4-1}+2x^{2-1}-7x^{1-1}$$

Subtract 1 from 4.

$$8x^{3}+2x^{2-1}-7x^{1-1}$$

Subtract 1 from 2.

$$8x^{3}+2x^{1}-7x^{1-1}$$

Subtract 1 from 1.

$$8x^{3}+2x^{1}-7x^{0}$$

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

$$8x^{3}+2x-7x^{0}$$

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

$$8x^{3}+2x-7$$