Solve (3x^3+4x+14)+(-4x^2+21)

$$( 3 x ^ { 3 } + 4 x + 14 ) + ( - 4 x ^ { 2 } + 21 )$$

Differentiate w.r.t. x

$$9x^{2}-8x+4$$

Steps Using Derivative Rule for Sum

Add 14 and 21 to get 35.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}+4x+35-4x^{2})$$

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}.

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

Multiply 3 times 3.

$$9x^{3-1}+4x^{1-1}+2\left(-4\right)x^{2-1}$$

Subtract 1 from 3.

$$9x^{2}+4x^{1-1}+2\left(-4\right)x^{2-1}$$

Subtract 1 from 1.

$$9x^{2}+4x^{0}+2\left(-4\right)x^{2-1}$$

Multiply 1 times 4.

$$9x^{2}+4x^{0}-8x^{2-1}$$

Subtract 1 from 2.

$$9x^{2}+4x^{0}-8x^{1}$$

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

$$9x^{2}+4x^{0}-8x$$

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

$$9x^{2}+4\times 1-8x$$

For any term t, t\times 1=t and 1t=t.

$$9x^{2}+4-8x$$

Evaluate

$$3x^{3}-4x^{2}+4x+35$$

Solution Steps

Add 14 and 21 to get 35.

$$3x^{3}+4x+35-4x^{2}$$