Question

find the differentiation with respect to x​

Answer 1

Answer:

your answer attached in the photo

Answer 2

$\huge{\underline{\underline{\red{♡Solution→}}}}$

Let,

$y = \frac{( {2 {x}^{2} - 7) }^{2} }{ {x}^{4} }$

$y = \frac{4 {x}^{4} + 49 - 2 \times 2 {x}^{2} \times 7 }{ {x}^{4} } \\ y = \frac{4 {x}^{4} - 28 {x}^{2} - 49 }{ {x}^{4} }$

By Differentiating -

$\frac{dy}{dx} = \frac{4 \times 4 \times {x}^{4 - 1} - 28 \times 2x + 0}{4 {x}^{4 - 1} } \\ \frac{dy}{dx} = \frac{16 {x}^{3} - 56x}{4 {x}^{3} } \\ \frac{dy}{dx} = \frac{x(16 {x}^{2} - 56) }{4 {x}^{3} } \\ \frac{dy}{dx} = \frac{16 {x}^{2} - 56}{4 {x}^{2} } \\ \frac{dy}{dx} = \frac{4(4x -14) }{4 {x}^{2} } \\ \frac{dy}{dx} = \frac{4x</strong><strong>^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong> - 14}{</strong><strong>x^</strong><strong>{</strong><strong>2</strong><strong>}</strong><strong>}$

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