Solve 4x^6+2x^4-x^2divx+1

$$4 x ^ { 6 } + 2 x ^ { 4 } - x ^ { 2 } \div x + 1$$

Evaluate

$$4x^{6}+2x^{4}-x+1$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$4x^{6}+2x^{4}-x^{1}+1$$

Calculate x to the power of 1 and get x.

$$4x^{6}+2x^{4}-x+1$$

Differentiate w.r.t. x

$$24x^{5}+8x^{3}-1$$

Steps Using Derivative Rule for Sum

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{6}+2x^{4}-x^{1}+1)$$

Calculate x to the power of 1 and get x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{6}+2x^{4}-x+1)$$

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}.

$$6\times 4x^{6-1}+4\times 2x^{4-1}-x^{1-1}$$

Multiply 6 times 4.

$$24x^{6-1}+4\times 2x^{4-1}-x^{1-1}$$

Subtract 1 from 6.

$$24x^{5}+4\times 2x^{4-1}-x^{1-1}$$

Multiply 4 times 2.

$$24x^{5}+8x^{4-1}-x^{1-1}$$

Subtract 1 from 4.

$$24x^{5}+8x^{3}-x^{1-1}$$

Subtract 1 from 1.

$$24x^{5}+8x^{3}-x^{0}$$

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

$$24x^{5}+8x^{3}-1$$