University:
Missouri State University
Course:
MTH 136 | Precalculus 1
Academic year:

2020
Views:

485

Pages:

2
Author:

catfever701r

Calculus Logarithmic Differentiation Worksheet Name Key Find the derivative of each function using logarithmic differentiation. 1. y = (3x - 7) ^ 4 * (8x ^ 2 - 1) ^ 3 ln(y) = 4in(3x - 7) + 3 * ln(8x ^ 2 - 1) 1/y * d/dx (x) = 4 * 3/(3x - 7) + 3 - (1l0x)/(8x ^ 2 - 1) 1/y * d/dx (y) = 12/(3x - 7) + (49x)/(8x ^ 2 - 1) d/dx (y) = (12/(3x - 7) + (48x)/(8x ^ 2 - 1)) * (3x - 7) ^ 4 * (8x ^ 2 - 1) ^ 3 2. y = x ^ (2/5) * (x ^ 2 + 8) * e ^ (x ^ 2 + x) lny= 2 5 ln x+ln(x^ 2 + overline 5 )+ (x ^ 2 + x) * in ln(y) = 2/5 * ln(x) + ln(x ^ 2 + 8) + x ^ 2 + x 1/y * (cdy)/(dx) = 2/5 * 1/x + (2x)/(x ^ 2 + 5) + 2x + 1 dy dx = (2/(5x) + (2x)/(x ^ 2 + 8) + 2x + 1) x^ 4)5 (x^ 4 +8)e^ x^ 2 +x 3. y = ((x + 1) ^ 4 * (x - 5) ^ 3)/((x - 3) ^ 8) |m| = 4 * ln(x + 1) + 3 * ln(x - 5) - 8 * ln(x - 3) 1/V * d/dx (v) = 4 * 1/(x + 1) + 3 * i/(x - 5) - 8 * i/(x - 3) d/dx (y) = (4/(x + 1) + 3/(x - 5) - 8/(x - 3)) * ((x + 1) ^ 4 * (x - 5) ^ 9)/((x - 3) ^ 8) 4. \mathcal{p} = sqrt((x ^ 2 + 1)/(x + 1)) y = ((x ^ 2 + 1) ^ (1/2))/((x + 1) ^ (1/2)) ln(gamma) = 1/2 * ln(x ^ 2 + 1) - 1/2 * ln(x + 1) 1/Y * d/dx (chi) = 1/Z * (Zx)/(x ^ 2 + i) - 1/2 * 1/(x + i) d/dx (y) = (x/(x ^ 2 + 1) - 1/(2(x + 1))) * ((x ^ 2 + i) ^ (1/2))/((x + i) ^ (1/2)) 5. y = x ^ x ln(y) = x * ln(x) 1/Y * d/dx (y) = (1) * ln(x) + (x)(1/x) d/dx (y) = (ln(x) + 1) * x ^ x 7. y = x ^ (sin x) ln(y) = sin x * ln(x) ((dy)/(dx) = (cos x)) * nx + (5sin x)(1/x) dx =(cosx Inx + sinx) x SinX 9. y = (ln(x)) ^ x 1ny = x * ln(ln(x)) 1/Y * d/dx (y) = (i) * ln(ln(x)) + (x)(1/x/(ln(x))) d/dx (y) = (ln(ln(x)) + i/(ln(x))) * (ln(x)) ^ x 11. Find d/dx (y) y = ln(x ^ 2 + y ^ 2) d/dx (y) = (2x + 2y * (v + 1)/(c + x))/(x ^ 2 + y ^ 2) (x ^ 2 + y ^ 2) * d/dx (y) = 2x + 2y * d/dx (y) (x ^ 2 + y ^ 2) * d/dx (y) - 2y * d/dx (y) = 2x そ 6. y = x ^ (y/x) ln(gamma) = 1/x * ln(x) Iny = x ^ - 1 * ln(x) 1/y * d/dx (y) = (- x ^ - 2) * ln(x) + (x ^ - 1)(1/x) d/dx (y) = (- (- i * nx)/(kappa ^ 2) + i/(x ^ 2)) * X ^ (1 / x) d/dx (y) = ((i - inx)/(x ^ 2)) * x ^ (i / x) مر 8. y = (sin x) ^ x Iny = x * ln(sin x) 1/y * d/dx (y) = (i) * ln(sin x) + (x) * (cos x)/(sin x) d/dx (y) = (ln(sin x) + xcstx) * (sin x) ^ x 10. y = x ^ ln(x) Iny = Inx.10x 1 Y dV dx =( 1 8 )( 0x + lox(1/8) d/dx (y) = ((2inx)/x) * x ^ (inx) Y = (inx)² 1/y * d/dx (y) = 2 * (ln(x))' * (1/x) d/dx (y) = ((2 * ln(x))/x) * x ^ ln(x) A