Question

Determine dy/dx for the following:
1.y=e^3x.cos(x^2+1)
2.y=ln(sqrt e^3x(x^2-1))

Answer 1

Just remember the chain and product rule, for the first problem we have
\[ \frac{dy}{dx} =\frac{d}{dx}[e^{3x}\cos(x^2+1)] \\
=\frac{d}{dx}[e^{3x}]\cos(x^2+1)+e^{3x}\frac{d}{dx}[\cos(x^2+1)] \\
=3e^{3x}\cos(x^2+1)+e^{3x}(-\sin(x^2+1)*2x) \\
=e^{3x}(3\cos(x^2+1)-2x\sin(x^2+1))
\]

Answer 2

Try to do the second problem yourself

Answer 3

Ok thank you,your a star! Just wanted to make sure my answers are right :)

Answer 4

No problem, glad to help!