Question

find dy/dx Y=x5+x3+10​

Answer 1

Answer:

5x^4 + 3x^2

Explanation:

Power Rule:

Take the exponent, multiply it by the coefficient (the number in front of the x), and decrease the exponent by 1.

x^5 = 1x5(x^(5-1)) = 5x^4

x^3 = 1x3(x^(3-1)) = 3x^2

10 = 1x0(x^(0-1)) = 0

Answer 2

Answer:

The value of $\frac{dy}{dx}$ Y= x⁵ + x³ + 10 is:

$\frac{dy}{dx}(Y)= 5x^{4} + 3x^{2}$

Explanation:

Here we have to use the identity:

$d(x^{n} )= nx^{n-1}$

Thus, applying the following identity of differential calculus for solving the given equation, we get,

Y= x⁵ + x³ + 10

⇒ d(Y)= d(x⁵ + x³ + 10)

⇒ $\frac{dy}{dx}(Y)= d(x^{5}) + d(x^{3}) + d(10)$

⇒ $\frac{dy}{dx}(Y)= 5x^{4} + 3x^{2} + 0$ [∵ $\frac{d}{dx} (C) = 0$]

⇒ $\frac{dy}{dx}(Y)= 5x^{4} + 3x^{2}$

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