Solve (10x^3-4x+11)+(9x^3+3x^2-2x+4)

$$( 10 x ^ { 3 } - 4 x + 11 ) + ( 9 x ^ { 3 } + 3 x ^ { 2 } - 2 x + 4 )$$

Evaluate

$$19x^{3}+3x^{2}-6x+15$$

Solution Steps

Combine 10x^{3} and 9x^{3} to get 19x^{3}.

$$19x^{3}-4x+11+3x^{2}-2x+4$$

Combine -4x and -2x to get -6x.

$$19x^{3}-6x+11+3x^{2}+4$$

Add 11 and 4 to get 15.

$$19x^{3}-6x+15+3x^{2}$$

Differentiate w.r.t. x

$$57x^{2}+6x-6$$

Steps Using Derivative Rule for Sum

Combine 10x^{3} and 9x^{3} to get 19x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(19x^{3}-4x+11+3x^{2}-2x+4)$$

Combine -4x and -2x to get -6x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(19x^{3}-6x+11+3x^{2}+4)$$

Add 11 and 4 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x}(19x^{3}-6x+15+3x^{2})$$

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}.

$$3\times 19x^{3-1}-6x^{1-1}+2\times 3x^{2-1}$$

Multiply 3 times 19.

$$57x^{3-1}-6x^{1-1}+2\times 3x^{2-1}$$

Subtract 1 from 3.

$$57x^{2}-6x^{1-1}+2\times 3x^{2-1}$$

Subtract 1 from 1.

$$57x^{2}-6x^{0}+2\times 3x^{2-1}$$

Multiply 1 times -6.

$$57x^{2}-6x^{0}+6x^{2-1}$$

Subtract 1 from 2.

$$57x^{2}-6x^{0}+6x^{1}$$

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

$$57x^{2}-6x^{0}+6x$$

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

$$57x^{2}-6+6x$$