Question

Find dy/dx if y=x10 +10x+ex

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Answer 1

Answer:

10x⁹ + 10ˣ log10 + eˣ

Or

10x⁹ + 10 + eˣ

Step-by-step explanation:

Given---> y = x¹⁰ + 10ˣ + eˣ

To find---> Derivative of given function

Solution----> We know that,

d / dx ( xⁿ ) = n xⁿ⁻¹

d / dx ( aˣ ) = aˣ loga

d / dx ( eˣ ) = eˣ

Now returning to original problem we get,

y = x¹⁰ + 10ˣ + eˣ

Differentiating with respect to x , we get

=> dy/dx = d / dx ( x¹⁰ + 10ˣ + eˣ )

= d / dx ( x¹⁰ ) + d/dx ( 10ˣ ) + d/dx ( eˣ )

Applying above formulee , we get

= 10 x¹⁰⁻¹ + 10ˣ log10 + eˣ

=>dy / dx= 10 x⁹ + 10ˣ log10 + eˣ

If question is like this ,

y = x¹⁰ + 10x + eˣ

Differentiating with respect to x, we get,

dy / dx = d/dx ( x¹⁰ ) + d/dx ( 10 x ) + d/dx ( eˣ )

= 10 x¹⁰⁻¹ + 10 ( 1 ) + eˣ

= 10 x⁹ + 10 + eˣ