Differentiation - Maharashtra Board STD 12 Science Maths Questions

If $y=f(u)$ is a differentiable function of $u$ and $u=g(x)$ is a differentiable function of $x$ such that the composite function $y=f[g(x)]$ is a differentlable function of $x$ then prove that
$\frac{d y}{d x}=\frac{d y}{d u} \times \frac{d u}{d x}$
Hence find $\frac{d y}{d x}$ if $y=\sqrt{x^2+5}$

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Q 14Solve the Following Question.(4 Marks)4 Marks

If $x=f(t), y=g(t)$ are differentiable functions of parameter ' $t$ ' then prove that $y$ is a differentiable function of ' $x$ ' and $\frac{d y}{d x}=\frac{\left(\frac{d y}{d t}\right)}{\left(\frac{d x}{d t}\right)}, \frac{d x}{d t} \neq 0$. Hence find $\frac{d y}{d x}$ if $x=a \cos t, y=a \sin t$.

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Q 15Solve the Following Question.(4 Marks)4 Marks

If $\sqrt{1-x^2}+\sqrt{1-y^2}=a(x-y)$, show that $\frac{d y}{d x}=\sqrt{\frac{1-y^2}{1-x^2}}$

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Q 16Solve the Following Question.(4 Marks)4 Marks

If $x=f(t)$ and $y=g(t)$ are differentiable function of $t$ so that $y$ is a differentiable function of $x$ and $\frac{d x}{d t} \neq 0$, then prove that :
$\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}$
Hence find $\frac{d y}{d x}$ if $x=\sin t$ and $y=\operatorname{cost} t$.

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Q 17Solve the Following Question.(4 Marks)4 Marks

If $x=f(t)$ and $y=g(t)$ are differentiable function of $t$, then prove that $y$ is a differentlable function of $x$ and $\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}$, where $\frac{d x}{d t} \neq 0$. Hence find $\frac{d y}{d x}$ if $x=a \cos ^2 t$ and $y=a \sin ^2 t$

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Differentiation question types

Differentiation questions

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Differentiation Maths - Differentiation

Differentiation question types

Differentiation questions

Generate a Differentiation paper free