## Brooke_army 2 years ago If y=x3+5x and dx/dt=5, find dy/dt when x=2.

1. Brooke_army

ok for this question i think im doing something wrong i got the answer of 17 but this is not right please help

2. nubeer

can you find dy/dx of the given equation?

3. Brooke_army

dy/dt=3x^2+5

4. phi

when you take the derivative wrt to t you should get a dx/dt term

5. hartnn

u need to use chain rule d/dt(5x) = 5 d/dx (dx/dt)

6. phi

instead of d/dx x^3 = 3 x^2 dx/dx you do d/dt x^3 = 3 x^2 dx/dt

7. phi

if you think $\frac{d}{dx} x= 1$ think this $\frac{ d}{dx} x= \frac{dx}{dx}= 1$

8. sunnymony

|dw:1352559750685:dw|

9. phi

using the same logic $\frac{d }{dt} x= \frac{dx}{dt}$

10. sunnymony

3x2+5 is ans

11. Brooke_army

thanks so much i got the wright answer!!

12. sunnymony

dy/dx= 3x2+5 dx/dt = 5 so both multiply we get =15x2+25

13. phi

then you got dy/dt=3x^2 dx/dt + 5 dx/dt replace x=2, dx/dt=5 to get dy/dt = 3*4*5+ 5*5= 85

14. sunnymony

so 15( 2x2)+25 =60+25 85

15. sunnymony

thats right @phi