Answer:
By definition, the derivative of f(x) is
![lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}](https://tex.z-dn.net/?f=lim_%7Bh%5Crightarrow%200%7D%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%7D%7Bh%7D)
Let's use the definition for ![f(x)=\frac{1}{x}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7B1%7D%7Bx%7D)
![lim_{h\rightarrow 0} \frac{\frac{1}{x+h}-\frac{1}{x}}{h}=\\lim_{h\rightarrow 0} \frac{\frac{x-(x+h)}{x(x+h)}}{h}=\\lim_{h\rightarrow 0} \frac{\frac{(-1)h}{x^2+xh}}{h}=\\lim_{h\rightarrow 0} \frac{(-1)h}{h(x^2+xh)}=\\lim_{h\rightarrow 0} \frac{-1}{x^2+xh)}=\frac{-1}{x^2+x*0}=\frac{-1}{x^2}](https://tex.z-dn.net/?f=lim_%7Bh%5Crightarrow%200%7D%20%5Cfrac%7B%5Cfrac%7B1%7D%7Bx%2Bh%7D-%5Cfrac%7B1%7D%7Bx%7D%7D%7Bh%7D%3D%5C%5Clim_%7Bh%5Crightarrow%200%7D%20%5Cfrac%7B%5Cfrac%7Bx-%28x%2Bh%29%7D%7Bx%28x%2Bh%29%7D%7D%7Bh%7D%3D%5C%5Clim_%7Bh%5Crightarrow%200%7D%20%5Cfrac%7B%5Cfrac%7B%28-1%29h%7D%7Bx%5E2%2Bxh%7D%7D%7Bh%7D%3D%5C%5Clim_%7Bh%5Crightarrow%200%7D%20%5Cfrac%7B%28-1%29h%7D%7Bh%28x%5E2%2Bxh%29%7D%3D%5C%5Clim_%7Bh%5Crightarrow%200%7D%20%5Cfrac%7B-1%7D%7Bx%5E2%2Bxh%29%7D%3D%5Cfrac%7B-1%7D%7Bx%5E2%2Bx%2A0%7D%3D%5Cfrac%7B-1%7D%7Bx%5E2%7D)
Then, ![f'(x)=\frac{-1}{x^2}](https://tex.z-dn.net/?f=f%27%28x%29%3D%5Cfrac%7B-1%7D%7Bx%5E2%7D)
Answer:
(- 1/2 * -2x) + (-1/2 * 4y)
(-1/4 * -8x)+(-1/4 * 12y)
Step-by-step explanation:
Hope this helps :)
Exact form:
x = -7/3
decimal form:
x = -2.3
mixed number form:
x = -2 1/3
Answer:
its A
Step-by-step explanation:
Answer:
sure, the answer is 50
Step-by-step explanation: Because this is a right triangle, you can use the pythagorean theorem, which is a^2 + b^2 =c^2 so you square 48 and add it to 14 squared and then take the square roo t to get the value of the hypotenuse, note that c will always represent the hypotenuse or longest side, and that pythagorean theorem can only be used on right triangles