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Derivative Rules Review Flashcards | StudBud

Explore/Derivative Rules Review

Derivative Rules Review

14 terms·StudBud Administration·4 plays

A beginning review of derivatives #calculus #derivatives

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Questions 14

Answers

1
Given f\left(x\right)=\frac{2}{5x^3+5}, find f'\left(x\right)
f'\left(x\right)=-\frac{2\cdot15x^2}{5x^3+5}
f'\left(x\right)=-\frac{2\cdot15x^2}{\left(5x^3+5\right)^2}
f'\left(x\right)=-\frac{15x^2}{\left(3x^3+5\right)^2}
f'\left(x\right)=-\frac{2\cdot15x^2}{2^2}
2
The second derivative of y=sin x is?
cos(x)
-sin(x)
six(n)
-cos(x)
3
Find the derivative of x=y^2+1 in terms of x
\frac{dy}{dx}=2y
\frac{dy}{dx}=\frac{x}{y^2+1}
\frac{dy}{dx}=-\frac{1}{y^2+1}
\frac{dy}{dx}=\frac{1}{2y}
4
The derivative of f(x)=e^3x-4 is?
e3x-4
3xe3x-4
ex e3x-4
3e3x-4
5
The second derivative of h(x)=e^6x is?
36e6x
12e6x
12ex
6e6x
6
The derivative of y=sin²(3x) is?
sin2(3x)cos(3x)(3)
2sin(3x)(cos(3x))(3)
sin(cos(tan(x)))
2cos(3x)(3)
7
Find the derivative of 3x-2y^3=5 with respect to x
\frac{dy}{dx}=-\frac{3}{5}
\frac{dy}{dx}=\frac{1}{2y^2}
\frac{dy}{dx}=2y^2
\frac{dy}{dx}=\frac{3x-2y^3}{5}
8
The derivative of f(x)=sec(8x-3) is?
sec(8x-3)(8)
sec(8x-3)tan(8x-3)(8)
sec(8x)tan(8x)(8x-3)
sec(8x-3)tan(8x-3)(8x)
9
The derivative of g(x)=ln(4x-9) is?
ln(4x-9)
(4x-9)(ln 4)
4/(4x-9)
ln(4)(4x-9)
10
What is the derivative of y=xsinx?
y'=cosx+xsinx
y'=xcosx+sinx
y'=sinxcosx
y'=1cosx
11
The second derivative of 6x is?
6x
0
1
6
12
The third derivative of 12x^4 is
288
144x^2
288x
48x^3
13
Find the derivative of 5=4x^2-y^3 with respect to x
\frac{dy}{dx}=\frac{8x}{4x^2-y^3}
\frac{dy}{dx}=\frac{8x}{3y^2}
\frac{dy}{dx}=\frac{5}{4x^2-y^3}
\frac{dy}{dx}=\frac{3y^2}{8x}
14
The derivative of 13x⁴ is?
13x3
54x3
42x4
52x3