Question

Помогите срочно. Желательно с подробным решением.

Answer 1

1. $f' = frac{1}{5} x^frac{-4}{5} + 2*3x^2-4 = frac{1}{5sqrt[5]{x^4} } +6x^2-4\f'(1) = frac{1}{5} +6-4=frac{11}{5}$

2. $f' = frac{frac{1}{2sqrt{x} }(3x+1)-sqrt{x} *3 }{(3x+1)^2} = frac{frac{3x+1-6x}{2sqrt{x} } }{(3x+1)^2} = frac{1-3x}{2sqrt{x} (3x+1)^2} \f'(2) = frac{1-6}{2sqrt{2} (6+1)^2} = frac{-5}{98sqrt{2} }$

3. $f' = 4*3x^2e^x-4x^3e^x = 12x^2e^x-4x^3e^x = 4x^2e^x(3-x)$

4. $f' = frac{1}{3x^2-4x} (3*2x-4)=frac{6x-4}{3x^2-4x}$

5. $f' = 4cos5x*5 = 20cos5x\f'(frac{pi }{2} )= 20cosfrac{5pi }{2} = 0$

6. $f' = frac{1}{1+(sqrt{6x-1})^2 } *frac{1}{2sqrt{6x-1} } *6=frac{1}{2xsqrt{6x-1} }$