Given y=2x^4-1+x^1/2, solve dy/dx

Using the sum rule, you can split the function in three terms and then derive each of them separately. The rule is to bring down the power and the power minus one. So for the first term, it becomes 2*4x^4-1, which is 8x³. Deriving a number, it becomes zero. The third one is (1/2)x^(1/2)-1, which becomes (1/2)x^^-1/2. So the result is dy/dx=8x³+(1/2)x^-1/2.