Looking for reliable answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
The derivative of the function is dy/dx = 4([tex]x^{4sinx}[/tex])[(sin x) / x + (cos x) (ln x)]
y = [tex]x^{4sin x}[/tex]
Taking the log of both sides:
ln y = sin x ln [tex]x^{4}[/tex] = (sin x) * (4 ln x) = 4 (sin x)(ln x)
Now differentiate both sides. On the left you'll need to use the chain rule, and on the right you'll use the product rule:
1/y dy/dx = 4[(sin x) (1/x) + (cos x)(ln x)] = 4 [(sin x) / x + (cos x)(ln x)]
Multiply both sides by y
dy/dx = y * 4 [(sin x) / x + (cos x)(ln x)]
Since y = [tex]x^{4sinx}[/tex], we can rewrite this as:
dy/dx = [tex]x^{4sinx}[/tex] * 4 [(sin x) / x + (cos x)(ln x)]
dy/dx = 4[tex]x^{4sinx}[/tex] [(sin x) / x + (cos x)(ln x)]
Chain rule is the formula used to find the derivative of a composite function. Product rule is used to find derivative of products of two or more functions.
Therefore, the derivative of the function y = [tex]x^{4sin x}[/tex] is dy/dx = 4([tex]x^{4sinx}[/tex])[(sin x) / x + (cos x) (ln x)]
To know more about derivative of the function
https://brainly.com/question/25752367
#SPJ4
Thanks for using our platform. We're always here to provide accurate and up-to-date answers to all your queries. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.
