If y = a^x cdot b^{2x-1},then frac{d^2 y}{d x | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Given $y = a^x \cdot b^{2x-1}$.We can rewrite this as $y = a^x \cdot (b^2)^x \cdot b^{-1} = \frac{1}{b} (a b^2)^x$.Taking the natural logarithm on

Vedclass · Accepted Answer

$y(\log(a b^2))^2$

Vedclass · Answer

(C) Given $y = a^x \cdot b^{2x-1}$.We can rewrite this as $y = a^x \cdot (b^2)^x \cdot b^{-1} = \frac{1}{b} (a b^2)^x$.Taking the natural logarithm on both sides: $\log y = \log \left( \frac{1}{b} (a b^2)^x \right) = \log(1) - \log(b) + x \log(a b^2) = -\log b + x \log(a b^2)$.Differentiating with respect to $x$: $\frac{1}{y} \frac{dy}{dx} = \log(a b^2)$.So,$\frac{dy}{dx} = y \log(a b^2)$.Differentiating again with respect to $x$: $\frac{d^2 y}{d x^2} = \frac{dy}{dx} \log(a b^2)$.Substituting $\frac{dy}{dx} = y \log(a b^2)$,we get $\frac{d^2 y}{d x^2} = (y \log(a b^2)) \cdot \log(a b^2) = y(\log(a b^2))^2$.

If $y = a^x \cdot b^{2x-1}$,then $\frac{d^2 y}{d x^2}$ is equal to

Similar Questions

If $x^{2} y^{5}=(x+y)^{7}$,then $\frac{d^{2} y}{d x^{2}}$ is equal to

$f(x) = e^x \sin x$,then $f^{(6)}(x)$ is equal to :

If $y = (\sin^{-1} 2x)^2 + (\cos^{-1} 2x)^2$, then $(1 - 4x^2) y_2 - 4x y_1 = $

If $y^{1/4} + y^{-1/4} = 2x$,and $(x^2 - 1) \frac{d^2y}{dx^2} + \alpha x \frac{dy}{dx} + \beta y = 0$,then $|\alpha - \beta|$ is equal to ...... .

If $y = a{e^{mx}} + b{e^{ - mx}}$,then $\frac{d^2y}{dx^2} - m^2y = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module