Math  /  Calculus

QuestionUse logarithmic differentiation to find the derivative of the function. y==(x5+2)2(x4+4)4y^{\prime}=\square=\left(x^{5}+2\right)^{2}\left(x^{4}+4\right)^{4} Need Help? Watch it

Studdy Solution
Substitute back y=(x5+2)2(x4+4)4 y = (x^5 + 2)^2 (x^4 + 4)^4 :
y=(x5+2)2(x4+4)4(10x4x5+2+16x3x4+4) y' = (x^5 + 2)^2 (x^4 + 4)^4 \left( \frac{10x^4}{x^5 + 2} + \frac{16x^3}{x^4 + 4} \right)
Solution: The derivative of the function y=(x5+2)2(x4+4)4 y = (x^5 + 2)^2 (x^4 + 4)^4 is:
y=(x5+2)2(x4+4)4(10x4x5+2+16x3x4+4) y' = (x^5 + 2)^2 (x^4 + 4)^4 \left( \frac{10x^4}{x^5 + 2} + \frac{16x^3}{x^4 + 4} \right)

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