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 $f(x) = 3x^3 + 2x^2 f'(1) + x f''(2) + f'''(3)$,then $f(x) = $

If $\log _e y=3 \sin ^{-1} x$,then $(1-x^2) y^{\prime \prime}-x y^{\prime}$ at $x=\frac{1}{2}$ is equal to :

If $y = a{x^{n + 1}} + b{x^{ - n}}$,then ${x^2}\frac{{{d^2}y}}{{d{x^2}}} = $

If $y=x \log \left(\frac{1}{a x}+\frac{1}{a}\right)$,then $x(x+1) \frac{d^2 y}{d x^2}+x \frac{d y}{d x}-y=$

If $f(x) = 10 \cos x + (13 + 2x) \sin x$, then $f''(x) + f(x)$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module