f'(x) = sec^2(x). At x = π/4, f'(π/4) = sec^2(π/4) = 2.

The derivative f'(x) = d/dx(tan(x)) = sec^2(x).

The derivative f'(x) = d/dx(tan(x)) = sec^2(x).

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

Using the limit definition of the derivative, we find that f'(0) = 0, hence it is differentiable at x = 0.

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

f'(x) = 3x^2 - 6x. At x = 2, f'(2) = 3(2^2) - 6(2) = 12 - 12 = 0.

Using the power rule, f'(x) = 3x^2 - 6x + 4.

Using the power rule, f'(x) = 3x^2 - 8x + 6.

Using the power rule, f'(x) = 4x^3 + 6x^2 - 1.

Using the power rule, f'(x) = 4x^3 - 12x^2 + 12x.

Using the power rule, f'(x) = 4x^3 - 12x^2 + 12x - 24.

The derivative f'(x) = d/dx(x^5 + 3x^3 - 2x) = 5x^4 + 9x^2 - 2.

Using the power rule, f'(x) = 5x^4 - 6x^2 + 1.

The derivative f'(x) = d/dx(x^5) - d/dx(3x) + d/dx(2) = 5x^4 - 3.

The derivative f'(x) = d/dx(x^5 - 3x^3 + 2) = 5x^4 - 9x^2.

Using the derivatives of sine and cosine, g'(x) = cos(x) - sin(x).

Determinant of E = 0 (rows are linearly dependent).

Det(E) = (3*4) - (2*1) = 12 - 2 = 10.

Det(E) = (4*3) - (2*1) = 12 - 2 = 10.

Det(F) = (4*1) - (3*2) = 4 - 6 = -2.

Det(F) = (4*7) - (5*6) = 28 - 30 = -2.

Determinant of G = (1*4) - (2*2) = 4 - 4 = 0.

Determinant of H = (3*5) - (1*2) = 15 - 2 = 13.

The determinant of J is calculated as (5*3) - (2*1) = 15 - 2 = 13.

The determinant of D can be calculated using the rule of Sarrus or cofactor expansion, which results in 0.

The determinant of D is calculated as (4*1) - (2*3) = 4 - 6 = -2.

The determinant of an upper triangular matrix is the product of its diagonal elements, which is 1.

Det(D) = (1*4) - (2*3) = 4 - 6 = -2.

The determinant is \( 3*4 - 2*1 = 12 - 2 = 10 \).