Question

If z=u+v, u=t², v=2t then dz/dt

Answer 1

Answer:

here, z=u+v

then, dz/dt = du/dt + dv/dt

dz/dt=d/dt(t^2) + d/dt (2t)

dz/dt= 2t + 2 d/dt t

dz/dt= 2t + 2

dz/dt = 2( t + 1 )

Answer 2

Answer:

as per the question we get,

$\frac{dz}{dt} = 2t+2$

Step-by-step explanation:

here in the given question we have given 3 functions and we have to differentiate and find the value of $\frac{dz}{dt}$

as per the question it is given that

z=u+v

and $u=t^2$

and v= 2t

so firstof all we will differentiate u and v with respect to t

so when we differentiate u with respect to t, we get $\frac{du}{dt}$

$u=t^2$

differentiating with respect to t,

$\frac{du}{dt} = 2t$

and similarly ,

so when we differentiate v with respect to t, we get $\frac{dv}{dt}$

we have given that v=2t

differentiating with respect to t,

$\frac{dv}{dt}= 2$

and now weve been given that z=u+v

now when we will differentiate with respect to t

$\frac{dz}{dt}= \frac{du}{dt} +\frac{dv}{dt}$

so by substituting the values

we get,

$\frac{dz}{dt} = 2t+2$

for more such questions you can visit:

https://brainly.in/question/8820108

#SPJ1