Find (d^(2))/(dx^(2))[e^(7x-4)] Choose 1 answer: (A) 7e^(7x-4) (B) 49e^(7x-4) (C) -16e^(7x) (D) 16e^(7x-4)

Differentiate Function: Differentiate the function e^(7x-4) with respect to x for the first time. The derivative of e^(u) with respect to x is u'e^(u), where u is a function of x and u' is the derivative of u with respect to x. Let u = 7x - 4, then u' = 7. (d)/(dx)(e^(7x-4)) = 7e^(7x-4)Find First Derivative: Differentiate the result from Step 1 with respect to x for the second time to find the second derivative. Again, we use the rule for differentiating e^(u), where u = 7x - 4 and u' = 7. (d^(2))/(dx^(2))(e^(7x-4)) = 7(d)/(dx)(e^(7x-4)) = 7 * 7e^(7x-4)Find Second Derivative: Simplify the expression from Step 2 to find the second derivative. (d^(2))/(dx^(2))(e^(7x-4)) = 49e^(7x-4)

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Find
(d^(2))/(dx^(2))[e^(7x-4)]
Choose 1 answer:
(A)
7e^(7x-4)
(B)
49e^(7x-4)
(C)
-16e^(7x)
(D)
16e^(7x-4)

Find $\frac{d^{2}}{d x^{2}}\left[e^{7 x-4}\right]$ $\newline$ Choose $1$ answer: $\newline$ (A) $7 e^{7 x-4}$ $\newline$ (B) $49 e^{7 x-4}$ $\newline$ (C) $-16 e^{7 x}$ $\newline$ (D) $16 e^{7 x-4}$

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Calculus

Find derivatives of using multiple formulae

Full solution

Q. Find

\frac{d^{2}}{d x^{2}}\left[e^{7 x-4}\right]

\newline

Choose

1

answer:

\newline

(A)

7 e^{7 x-4}

\newline

(B)

49 e^{7 x-4}

\newline

(C)

-16 e^{7 x}

\newline

(D)

16 e^{7 x-4}

Differentiate Function: Differentiate the function $e^{7x-4}$ with respect to $x$ for the first time. $\newline$ The derivative of $e^{u}$ with respect to $x$ is $u'e^{u}$ , where $u$ is a function of $x$ and $u'$ is the derivative of $u$ with respect to $x$ . $\newline$ Let $x$ $0$ , then $x$ $1$ . $\newline$ $x$ $2$
Find First Derivative: Differentiate the result from Step $1$ with respect to $x$ for the second time to find the second derivative. $\newline$ Again, we use the rule for differentiating $e^{u}$ , where $u = 7x - 4$ and $u' = 7$ . $\newline$ $\frac{d^{2}}{dx^{2}}(e^{7x-4}) = 7\frac{d}{dx}(e^{7x-4}) = 7 \times 7e^{7x-4}$
Find Second Derivative: Simplify the expression from Step $2$ to find the second derivative. $\newline$ $(\frac{d^2}{dx^2})(e^{7x-4}) = 49e^{7x-4}$