Find the derivative of y = sin(xe^x) with respect to x.

Q: Find the derivative of y = sin(xe^x) with respect to x.

Find the derivative of y = sin(xe^x) with respect to x. dy/dx = cos(xe^x)(e^x + xe^x) ✓ dy/dx = -cosec(xe^x)(e^x + xe^x) dy/dx = cos(xe^x)(xe^x) dy/dx = sec(xe^x)(e^x + xe^x) Explanation Depreciation (weaker currency): exports cheaper (more competitive), imports more expensive (encourages local production but raises input costs). Inflation may rise. Good for exporters, bad for importers. Appreciation (stronger currency): exports more expensive (less competitive), imports cheaper (lower inflation, cheaper inputs). Good for consumers buying imports, bad for export industries. Naira depreciation affects: fuel prices (imported), imported goods costs, foreign debt burden (pay more naira per dollar). Exchange rate stability important for business planning.

Question

Answer 1

Find the derivative of y = sin(xe^x) with respect to x.

dy/dx = cos(xe^x)(e^x + xe^x) ✓
dy/dx = -cosec(xe^x)(e^x + xe^x)
dy/dx = cos(xe^x)(xe^x)
dy/dx = sec(xe^x)(e^x + xe^x)

Explanation

Depreciation (weaker currency): exports cheaper (more competitive), imports more expensive (encourages local production but raises input costs). Inflation may rise. Good for exporters, bad for importers.

Appreciation (stronger currency): exports more expensive (less competitive), imports cheaper (lower inflation, cheaper inputs). Good for consumers buying imports, bad for export industries.

Naira depreciation affects: fuel prices (imported), imported goods costs, foreign debt burden (pay more naira per dollar). Exchange rate stability important for business planning.