Question

1-01
find derivative of the following
(1) y=x²+4x
(2) f(x) = sinx-3C0SX + Tanx
(3) y = 4 +3x power 10-x power 100
(4) y = 3 log x- 2rootx -5 power x


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Answer 1

Answer:

$1. \: y = {x}^{2} + 4x \\ \frac{dy}{dx} = 2x + 4 \\ 2. \: f(x )\: = \sin(x) - 3 \cos(x )+ \tan(x) \\ \frac{dy}{dx} = \cos(x) + 3 \sin(x) + { \sec(x) }^{2} \\ 3. \: y = 4 + {3x}^{10} - {x}^{100} \\ \frac{dy}{dx} = 30 {x}^{9} - 100 {x}^{99} \\ 4. \: y = 3 log(x) - 2 \sqrt{x} - {5}^{x} \\ \frac{dy}{dx} = \frac{3}{x} - \frac{1}{ \sqrt{x} } - 5 {}^{x} log(5)$

Answer 2

Answer:

1)- 2x+4

2)- 1+3sinx+sec^2x

3)-30x^9-100x^99

4)- 3rootx -2x/xrootx

Step-by-step explanation:

1) y=x^24x

=d/dx .x^2+d/dx .4x

=2x+4

2)d/dx .x-d/dx.3xcosx+d/dx.tanx

=1+3sinx+0+sec^2x

=1+3sinx+sec^2x.

3) =d/dx.4+d/dx3x^10-d/dx.x^100

=30x^9-100x^99

4)d/dx.3logx -d/dx2x^1/2-d/dx5^x

=3×1/x-2/rootx-0

=3/x-2/rootx