Question

using chain rule find dx/dy of y= u/5+7 and u=5x-35?

Answer 1

Conditions

using chain rule find $\frac{dx}{dy}$ of $y = \frac{u}{5 + 7}$ and $u = 5x - 35$ ?

Solution

In calculus, the chain rule is a formula for computing the derivative of the composition of two or more functions. That is, if $f$ is a function and $g$ is a function, then the chain rule expresses the derivative of the composite function $f \circ g$ in terms of the derivatives of $f$ and $g$ . For example, the chain rule for $f \circ g(x) \equiv f[g(x)]$ is

$$\frac {d f}{d x} = \frac {d f}{d g} \frac {d g}{d x}.$$ $$y [ u (x) ] = \frac {u (x)}{5} + 7$$ $$u (x) = 5 x - 3 5$$ $$\frac {d y}{d x} = \frac {d y}{d u} \frac {d u}{d x}$$ $$\frac {d y}{d u} = \left(\frac {u}{5} + 7\right) _ {u} ^ {s} = \frac {1}{5}$$ $$\frac {d u}{d x} = (5 x - 3 5) _ {x} ^ {s} = 5$$ $$\frac {d y}{d u} \frac {d u}{d x} = \frac {1}{5} 5 = 1$$

Answer: 1