Solve (x+4x^3+7)+(3x^3-9-3x)

$$( x + 4 x ^ { 3 } + 7 ) + ( 3 x ^ { 3 } - 9 - 3 x )$$

Evaluate

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

Solution Steps

Combine 4x^{3} and 3x^{3} to get 7x^{3}.

$$x+7x^{3}+7-9-3x$$

Subtract 9 from 7 to get -2.

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

Combine x and -3x to get -2x.

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

Differentiate w.r.t. x

$$21x^{2}-2$$

Steps Using Derivative Rule for Sum

Combine 4x^{3} and 3x^{3} to get 7x^{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+7x^{3}+7-9-3x)$$

Subtract 9 from 7 to get -2.

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

Combine x and -3x to get -2x.

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

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}.

$$-2x^{1-1}+3\times 7x^{3-1}$$

Subtract 1 from 1.

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

Multiply 3 times 7.

$$-2x^{0}+21x^{3-1}$$

Subtract 1 from 3.

$$-2x^{0}+21x^{2}$$

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

$$-2+21x^{2}$$