Please show a step by step methods of how it is done. Thank you

For each of the following functions, (1) derive the marginal rate of technical substitution, (2) say whether it exhibits diminishing marginal product of labor, and (3) say whether it exhibits increasing, decreasing or constant returns to scale. a. q=K+L10KL b. q=K2L c. q=min(3K,4L) d. For the functions in 2a,2b,2c, (1) Find the function for (or the value of) the elasticity of substitution for each production function and (2) find the cost minimizing input combination to produce 10 units of output when w=$1 and r=$4. e. For the function in part 2a above, derive the conditional factor demand functions. For each of the following functions, (1) derive the marginal rate of technical substitution, (2) say whether it exhibits diminishing marginal product of labor, and (3) say whether it exhibits increasing, decreasing or constant returns to scale. a. q=K+L10KL b. q=K2L c. q=min(3K,4L) d. For the functions in 2a,2b,2c, (1) Find the function for (or the value of) the elasticity of substitution for each production function and (2) find the cost minimizing input combination to produce 10 units of output when w=$1 and r=$4. e. For the function in part 2a above, derive the conditional factor demand functions