Chapter 4.4, Problem 43E

How to solve this using logarithmic differentiation?

Find the derivatives. Simplify the answer. Use logarithmic differentiation.

PLEASE DO IT ON PAPER. This is calculus show all work

stion Four: Find the second derivative of x = tan (y)

Please solve and show full work.

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EVALUATION Find the derivative of the given function. Fill the missing expressions. Use logarithmic differentiation. y = x· secx · Vx² + 1 Step 1. Take the absolute value of both sides. lyl = |x - secx · Jx2 + 1 Step 2. Take the natural logarithm of both sides. In ]y| = In x• secx · x2 + 1 Step 3. Expand using the properties of Logarithm Inlyl = Inx + In|secx| + Step 4. Differentiate both sides. D,(In\y\) = Dx Inx + In|secx| +In(x² + 1) 1 1 = -+ .· Dz(secx) + 1 Dz(x² + 1) 2 x2 + 1 1 1 · secx tanx +: 1 2x 2 x2 + 1 Step 5. Multiply both sides of the equation by y to solve for y' + tanx + (x² + 1) Step 6. Substitute y with the given function. 1 y' = + 5cotx + \3(x+ 1) (1 – x²).

Use logarithmic differentiation to find the derivative of y = sin(5x)1+5x y = 5*(1+5*x)*sin Your last answer was interpreted as follows: 5*(1+5*x)*sin This answer is invalid. Forbidden variable or constant: sin. Check

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