Question:
If $y=e^{3x+7}$, then the value of $\frac{dy}{dx} \bigg|_{x=0}$ is
If $y=e^{3x+7}$, then the value of $\frac{dy}{dx} \bigg|_{x=0}$ is
Updated On: Jul 6, 2022
- $1$
- $0$
- $-1$
- $3e^7$
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The Correct Option is D
Solution and Explanation
$\because y=e^{3x+7}\Rightarrow \frac{dy}{dx}=3e^{3x+7}$
$\therefore \frac{dy}{dx}\bigg|_{x=0}=3e^{3\times0+7}=3e^{7}$
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Notes on Continuity and differentiability
Concepts Used:
Continuity & Differentiability
Definition of Differentiability
f(x) is said to be differentiable at the point x = a, if the derivative f ‘(a) be at every point in its domain. It is given by
Definition of Continuity
Mathematically, a function is said to be continuous at a point x = a, if
It is implicit that if the left-hand limit (L.H.L), right-hand limit (R.H.L), and the value of the function at x=a exist and these parameters are equal to each other, then the function f is said to be continuous at x=a.
If the function is unspecified or does not exist, then we say that the function is discontinuous.