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# Solution for Find the Second Order Derivatives of the Following Function E6x Cos 3x ? - CBSE (Science) Class 12 - Mathematics

ConceptSimple Problems on Applications of Derivatives

#### Question

Find the second order derivatives of the following function e6x cos 3x  ?

#### Solution

We have,

$y = e^{6x} \cos 3x$

$\text { Differentiating w . r . t . x, we get }$

$\frac{d y}{d x} = e^{6x} \times 6 \times \cos 3x + e^{6x} ( - \sin 3x \times 3)$

$= 6 e^{6x} \cos3x - 3 e^{6x} \sin 3x$

$\text { Differentiating again w . r . t . x, we get }$

$\frac{d^2 y}{d x^2} = 6 e^{6x} \cos3x \times 6 - 6 e^{6x} \sin3x \times 3 - 3 \times 6 e^{6x} \sin3x - 3 e^{6x} \times 3 \cos 3x$

$= 27 e^{6x} \cos3x - 36 e^{6x} \sin3x$

$= 9 e^{6x} \left( 3 \cos3x - 4 \sin3x \right)$

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Solution Find the Second Order Derivatives of the Following Function E6x Cos 3x ? Concept: Simple Problems on Applications of Derivatives.
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