Question

the differenciation of y=8x8 with respect to X is 64xn then find the value of n

NOTE:Y=8x power 8.
X=64x power n​

Answer 1

$\Huge{\underline{\underline{\mathfrak{Answer \colon}}}}$

From the Question,

• $\sf{y = {8x}^{8}}$

• $\sf{y' = {64x}^{n}............(1)}$

To find

The value of 'n' for which the derivative of given number is 64xⁿ

Differentiating y w.r.t to x,we get :

$\sf{ \frac{dy}{dx} = \frac{d(8x {}^{8}) }{dx} } \\ \\ \sf{Using \: (1),} \\ \\ \implies \: \sf{64x {}^{n} = 8(8x) {}^{8 - 1} } \\ \\ \implies \: \sf{64x {}^{n} = 64x {}^{7} }$

Since,the bases are equal

$\huge{ \implies \: \mathtt{n = 7}}$

Thus,the required value of 'n' is 7

Answer 2

$\huge{\star}{\underline{\boxed{\red{\sf{Answer :}}}}}{\star}$

We are Given ,

$\Large{\sf{y \: = \: 8x^{8}}}$

$\Large{\sf{y' \: = \: 64x^{n}}}$

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Differentiate y with respect to x

$\LARGE{\sf{\frac{dy}{dx} \: = \: \frac{d(x^8)}{dx}}}$

Use value of y'

$\Large \leadsto {\sf{64^{n} \: = \: 8(8)x^{8 \: - \: 1}}}$

$\Large \leadsto {\sf{64^{n} \: = \: 64x^7}}$

Bases are same,

$\Huge \implies {\boxed{\boxed{\sf{n \: = \: 7}}}}$

∴ The value of n is 7