Use the chain rule to find fracdzdt when z = cos(x + 4y), x = 5t4, y = | Basic Mathematics 2081.2

Basic Mathematics2081.25 marksNumerical: chain rule derivativeChain rule

Use the chain rule to find $\frac{dz}{dt}$ when $z = \cos(x + 4y)$ , $x = 5t^4$ , $y = \frac{1}{t}$ . [5]

Use the chain rule to find $\frac{dz}{dt}$ when $z = \cos(x + 4y)$, $x = 5t^4$, $y = \frac{1}{t}$. [5]

$z = \cos(x + 4y)$ - $x = 5t^4$ - $y = \dfrac{1}{t}$ Required: $\dfrac{dz}{dt}$ All data present. --- $\frac{dz}{dt} = \frac{\partial z}{\partial x}\cdot\frac{dx}{dt} + \frac{\partial z}{\partial y}\cdot\frac{dy}{dt}$ $\frac{\partial z}{\partial x} = -\sin(x + 4y)$ $$\frac{\partial z}{\part...

$z = \cos(x + 4y)$ - $x = 5t^4$ - $y = \dfrac{1}{t}$ Required: $\dfrac{dz}{dt}$ All data present. --- $$\frac{dz}{dt} = \frac{\partial z}{\partial x}\cdot\frac{dx}{dt} + \frac{\partial z}{\partial y}\cdot\frac{dy}{dt}$$ $$\frac{\partial z}{\partial x} = -\sin(x + 4y)$$ $$\frac{\partial z}{\part...

Use the chain rule to find fracdzdt when z = cos(x + 4y), x = 5t4, y = frac1t.