Solve -6x^4+5x^2+1+11xtext{by}2x^2+1

$$- 6 x ^ { 4 } + 5 x ^ { 2 } + 1 + 11 x \text { by } 2 x ^ { 2 } + 1$$

Differentiate w.r.t. x

$$2x\left(5+33bxy-12x^{2}\right)$$

Steps Using Derivative Rule for Sum

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{4}+5x^{2}+1+11x^{3}by\times 2+1)$$

Multiply 11 and 2 to get 22.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{4}+5x^{2}+1+22x^{3}by+1)$$

Add 1 and 1 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-6x^{4}+5x^{2}+2+22x^{3}by)$$

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}.

$$4\left(-6\right)x^{4-1}+2\times 5x^{2-1}+3\times 22byx^{3-1}$$

Multiply 4 times -6.

$$-24x^{4-1}+2\times 5x^{2-1}+3\times 22byx^{3-1}$$

Subtract 1 from 4.

$$-24x^{3}+2\times 5x^{2-1}+3\times 22byx^{3-1}$$

Multiply 2 times 5.

$$-24x^{3}+10x^{2-1}+3\times 22byx^{3-1}$$

Subtract 1 from 2.

$$-24x^{3}+10x^{1}+3\times 22byx^{3-1}$$

Multiply 2 times 5.

$$-24x^{3}+10x^{1}+66byx^{3-1}$$

Subtract 1 from 3.

$$-24x^{3}+10x^{1}+66byx^{2}$$

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

$$-24x^{3}+10x+66byx^{2}$$

Evaluate

$$2+22byx^{3}+5x^{2}-6x^{4}$$