Question

If \(y=\frac{sin(x)e^x}{cos^2(x)}\), find ^dy⁄dx .

(a) Sec^2 (x) e^x [1 + Tan(x)] + e^x Tan(x)Sec(x)

(b) Sec^2 (x) e^x [Sec(x) + Tan(x)] + e^x Tan(x)Sec(x)

(c) Sec^2 (x) e^2x [Sec(x) + Tan(x)] + e^x Tan(x)Sec(x)

(d) Sec(x) e^x [Sec(x) + Tan(x)] + e^x Tan(x)Sec(x)

The question was posed to me in homework.

Enquiry is from Limits and Derivatives of Several Variables topic in division Partial Differentiation of Engineering Mathematics

Answer 1

Right option is (c) Sec^2 (x) e^2x [Sec(x) + Tan(x)] + e^x Tan(x)Sec(x)

Best explanation: \(y=\frac{sin(x)e^x}{cos^2(x)}\) = Tan(x)Sec(x) e^x

^dy⁄dx = Sec^2 (x)Sec(x) e^x + Sec^2 (x)Tan(x) e^x + e^x Tan(x)Sec(x)

^dy⁄dx = Sec^2 (x) e^x [Sec(x) + Tan(x)] + e^x Tan(x)Sec(x).