If u and v are differentiable functions of x and if y-u-v then dy dx - du dx - dv dx

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Standard XII

Mathematics

Algebra of Derivatives

If u and ...

Question

If $u$ and $v$ are differentiable functions of $x$ and if $y = u + v$ then $\frac{d y}{d x} = \frac{d u}{d x} + \frac{d v}{d x}$

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Solution

Let $y = u + v$ where $u, v$ are differentiable fuctions of $x$ .

Consider $y = u + v$

Differentiate both sides with respect to $x$ we get

$\frac{d y}{d x} = \frac{d u}{d x} + \frac{d v}{d x}$

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If u and v are differentiable functions of x and if y=u+v then dydx=dudx+dvdx

Let y=u+v where u,v are differentiable fuctions of x.Consider y=u+vDifferentiate both sides with respect to x we getdydx=dudx+dvdx

If $u$ and $v$ are differentiable functions of $x$ and if $y = u + v$ then $\frac{d y}{d x} = \frac{d u}{d x} + \frac{d v}{d x}$

Let $y = u + v$ where $u, v$ are differentiable fuctions of $x$ .

Consider $y = u + v$

Differentiate both sides with respect to $x$ we get

$\frac{d y}{d x} = \frac{d u}{d x} + \frac{d v}{d x}$