Solve -83^2-5*3+8left(x3right)^2+8

$$-8 { 3 }^{ 2 } -5 \times 3+8 { \left(x3 \right) }^{ 2 } +8$$

Evaluate

$$8x_{3}^{2}-79$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$-8\times 9-5\times 3+8x_{3}^{2}+8$$

Multiply -8 and 9 to get -72.

$$-72-5\times 3+8x_{3}^{2}+8$$

Multiply 5 and 3 to get 15.

$$-72-15+8x_{3}^{2}+8$$

Subtract 15 from -72 to get -87.

$$-87+8x_{3}^{2}+8$$

Add -87 and 8 to get -79.

$$-79+8x_{3}^{2}$$

Differentiate w.r.t. x_3

$$16x_{3}$$

Steps Using Derivative Rule for Sum

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(-8\times 9-5\times 3+8x_{3}^{2}+8)$$

Multiply -8 and 9 to get -72.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(-72-5\times 3+8x_{3}^{2}+8)$$

Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(-72-15+8x_{3}^{2}+8)$$

Subtract 15 from -72 to get -87.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(-87+8x_{3}^{2}+8)$$

Add -87 and 8 to get -79.

$$\frac{\mathrm{d}}{\mathrm{d}x_{3}}(-79+8x_{3}^{2})$$

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}.

$$2\times 8x_{3}^{2-1}$$

Multiply 2 times 8.

$$16x_{3}^{2-1}$$

Subtract 1 from 2.

$$16x_{3}^{1}$$

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

$$16x_{3}$$