Class 12

Math

Calculus

Differentiation

Differentiate $2_{x_{3}}$ with respect to $x$ :

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f(x) is a polynomial function, $f:R→R,$ such that $f(2x)=f_{′}(x)f_{′′}(x).$ Equation f(x) = x has (A) three real and positive roots (B) three real and negative roots (C) one real root (D) three real roots such that sum of roots is zero

A nonzero polynomial with real coefficients has the property that $f(x)=f_{′}(x)⋅f_{′′}(x).$ If a is the leading coefficient of f(x), then the value of $1/a$ is -

$y=sin_{−1}1+x_{2}2x ,−1≤x≤1$

Differentiate $gtan(4π +2x )$ with respect to $x$ :

Find $dxdy $ , when $y=cot2xsinx+x_{2} $

Differentiate $(g)_{x}2$ with respect to $x$ :

Find $dxdy ifx=3cosθ−2cos_{3}θ,y=3sinθ−2sin_{3}θ.$

$Prove thatϕ(x)=∣∣ f(x)f_{′}(x)f_{′′}(x) g(x)g_{′}(x)g_{′′}(x) h(x)h_{′}(x)h_{′′}(x) ∣∣ $ is a constant polynomial.