Given {eq}f(x)=3\sec(4x) {/eq}, find {eq}f''(x) {/eq}


Given {eq}f(x)=3\sec(4x) {/eq}, find {eq}f''(x) {/eq}

Second Order Derivatives:

To calculate the second order derivative of the function {eq}f(x) {/eq}, we must differentiate it twice.

Suppose its first derivative is denoted by {eq}f'(x) {/eq}.

Then the second derivative {eq}f''(x) {/eq} will be equivalent to:

{eq}f''(x) = \displaystyle D_x f'(x) {/eq}

Answer and Explanation: 1

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We derive the given function twice to obtain {eq}f''(x) {/eq}.

Obtaining first {eq}f'(x) {/eq} by deriving {eq}f(x) {/eq}:

{eq}\begin{align*} f(...

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Calculating Higher Order Derivatives


Chapter 8 / Lesson 10

Higher order derivatives, 2nd, 3rd, and 4th order derivatives, can be calculated using the change in rate of acceleration, known as 'jerk'. Learn how to find these higher order derivatives and the concept of 'jerk' in mathematics.

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