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

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

Evaluate

$$3x^{2}-194$$

Solution Steps

Multiply 2 and 2 to get 4.

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

Calculate -4 to the power of 3 and get -64.

$$4\left(-64\right)-\left(-4\right)^{3}+3x^{2}-2$$

Multiply 4 and -64 to get -256.

$$-256-\left(-4\right)^{3}+3x^{2}-2$$

Calculate -4 to the power of 3 and get -64.

$$-256-\left(-64\right)+3x^{2}-2$$

The opposite of -64 is 64.

$$-256+64+3x^{2}-2$$

Add -256 and 64 to get -192.

$$-192+3x^{2}-2$$

Subtract 2 from -192 to get -194.

$$-194+3x^{2}$$

Differentiate w.r.t. x

$$6x$$

Steps Using Derivative Rule for Sum

Multiply 2 and 2 to get 4.

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

Calculate -4 to the power of 3 and get -64.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4\left(-64\right)-\left(-4\right)^{3}+3x^{2}-2)$$

Multiply 4 and -64 to get -256.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-256-\left(-4\right)^{3}+3x^{2}-2)$$

Calculate -4 to the power of 3 and get -64.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-256-\left(-64\right)+3x^{2}-2)$$

The opposite of -64 is 64.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-256+64+3x^{2}-2)$$

Add -256 and 64 to get -192.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-192+3x^{2}-2)$$

Subtract 2 from -192 to get -194.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-194+3x^{2})$$

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}.

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

Multiply 2 times 3.

$$6x^{2-1}$$

Subtract 1 from 2.

$$6x^{1}$$

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

$$6x$$