Using the product rule, f'(x) = 2x * sin(x) + x^2 * cos(x).

Using the product rule, f'(x) = 3x^2 * e^x + x^3 * e^x.

Using the product rule, f'(x) = 3x^2 * ln(x) + x^2.

Using the power rule, f'(x) = 3x^2 - 4.

The derivative f'(x) = 3x^2 - 12x + 9.

Using the power rule, f'(x) = 4x^3 - 12x.

The derivative f'(x) = d/dx(3x^2 + 5x - 7) = 6x + 5.

The determinant of a 1x1 matrix is simply the value of the single element. Therefore, the determinant of [[5]] is 5.

The determinant of a 2x2 matrix is calculated as ad - bc.

The determinant of a 2x2 matrix is calculated as ad - bc.

The determinant of E is 0 because the rows are linearly dependent.

The determinant can be calculated using the formula for 3x3 matrices. Here, the first column is the same, leading to a determinant of 0.

The determinant is 0 because the first column is a linear combination of the other columns.

Det(J) = (5*8) - (6*7) = 40 - 42 = -2.

The direction of the magnetic field around a current-carrying conductor is given by the right-hand rule, which indicates a counterclockwise direction when viewed from the positive current side.

For the equation y^2 = 4px, p = 5. The directrix is given by x = -p, which is x = -5.

Using the distance formula: d = √[(3 - 0)² + (4 - 0)²] = √[9 + 16] = √25 = 5.

Using the distance formula: d = √((8 - 0)² + (6 - 0)²) = √(64 + 36) = √100 = 10.

Using the distance formula: d = √[(3 - 0)² + (4 - 0)²] = √[9 + 16] = √25 = 5.

Using the distance formula: d = √[(6 - 2)² + (7 - 3)²] = √[16 + 16] = √32 = 4√2 ≈ 5.66.

Using the distance formula: d = √[(3 - 3)² + (-2 - 2)²] = √[0 + 16] = √16 = 4.

Using the distance formula: d = √[(3 - 3)² + (1 - 7)²] = √[0 + 36] = √36 = 6.

Using the distance formula: d = √[(1 - 5)² + (1 - 5)²] = √[16 + 16] = √32 = 4√2.

Using the distance formula: d = √[(6 - 6)² + (2 - 8)²] = √[0 + 36] = √36 = 6.

The spreading out of sound waves after passing through a narrow opening is known as diffraction.

Adding a base to a weak acid will neutralize some of the acid, increasing the pH.

Adding a base to hydrochloric acid will neutralize it, resulting in an increase in pH.

Adding a base to an acidic solution increases the pH, making it less acidic.

Adding a strong acid to a weak base will decrease the pH of the solution.

Deforestation typically leads to increased temperatures in the local climate due to reduced transpiration and increased solar radiation absorption.