Solve 6x^4+8x^3+5x^2+20+50

$$6 x ^ { 4 } + 8 x ^ { 3 } + 5 x ^ { 2 } + 20 + 50$$

Differentiate w.r.t. x

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

Steps Using Derivative Rule for Sum

Add 20 and 50 to get 70.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{4}+8x^{3}+5x^{2}+70)$$

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}.

$$4\times 6x^{4-1}+3\times 8x^{3-1}+2\times 5x^{2-1}$$

Multiply 4 times 6.

$$24x^{4-1}+3\times 8x^{3-1}+2\times 5x^{2-1}$$

Subtract 1 from 4.

$$24x^{3}+3\times 8x^{3-1}+2\times 5x^{2-1}$$

Multiply 3 times 8.

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

Subtract 1 from 3.

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

Multiply 3 times 8.

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

Subtract 1 from 2.

$$24x^{3}+24x^{2}+10x^{1}$$

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

$$24x^{3}+24x^{2}+10x$$

Evaluate

$$6x^{4}+8x^{3}+5x^{2}+70$$

Solution Steps

Add 20 and 50 to get 70.

$$6x^{4}+8x^{3}+5x^{2}+70$$