Solve x^2(-1)(+3)*4^2(-4)=

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

Evaluate

$$192x^{2}$$

Solution Steps

Multiply -1 and 3 to get -3.

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

Calculate 4 to the power of 2 and get 16.

$$x^{2}\left(-3\right)\times 16\left(-4\right)$$

Multiply -3 and 16 to get -48.

$$x^{2}\left(-48\right)\left(-4\right)$$

Multiply -48 and -4 to get 192.

$$x^{2}\times 192$$

Differentiate w.r.t. x

$$384x$$

Steps Using Definition of a Derivative

Multiply -1 and 3 to get -3.

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

Calculate 4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\left(-3\right)\times 16\left(-4\right))$$

Multiply -3 and 16 to get -48.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\left(-48\right)\left(-4\right))$$

Multiply -48 and -4 to get 192.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\times 192)$$

The derivative of ax^{n} is nax^{n-1}.

$$2\times 192x^{2-1}$$

Multiply 2 times 192.

$$384x^{2-1}$$

Subtract 1 from 2.

$$384x^{1}$$

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

$$384x$$