dy/dx = (5x3 + 1)(15x4) + (3x5 + 1)(15x2)

y' = (-2x5)(5x4) + (x5 - 2)(-10x4), y' = -100x9 +20x4

f'(x) = -(5x4)(2x5 + 2)-2(10x4) + (2x5 + 1)-1(20x3), f'(x) = [(2x5 + 2)(20x3) - (5x4)(10x4)] / (2x5 + 2)2

y' = x(x2 + 1)(-1/2), y' = (1/2)(x2 + 1)(-1/2) (2x)

A derivative is also ________________

the slope., the instantaneous rate of change., the instantaneous velocity.

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Basic Derivatives Calculus Introduction

15 termsStudBud Administration

Basic Derivatives #powerrule #productrule #chainrule #calculus #tangentline #averagerateofchange #unsimplifed

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Questions 15

Answers

1
Find dy/dx.
dy/dx = 4(3x4 + 4)3 (12x3)
dy/dx = 4(3x4 + 4)3
dy/dx = 4(12x3)3
dy/dx = 4(3x4 + 4)3 + 12x3
2
The derivative is the _____________
average rate of change.
instantaneous velocity.
average velocity.
speed.
3
Find dy/dx.
dy/dx = (5x3 + 1) + (3x5 + 1)
dy/dx = (5x3 + 1)(15x4) - (3x5 + 1)(15x2)
dy/dx = (5x3 + 1)(15x4) + (3x5 + 1)(15x2)
dy/dx = (5x3 + 1)(15x4)(3x5 + 1)(15x2)
4
Find the equation of the TANGENT line to the function at the given point.
y = 4x +16
y = 8x +5
y = 8x +19
y = 8x - 26
5
Find the average rate of change of the function over the given interval.
1
-1
-3
-2
6
Find dy/dx .
y' = -2
y' = x
y' = 2x
y' = 2
7
Find dy/dx.
y' = -3( 3x4 - 5)-2 (12x3)
y' = -3( 3x4 - 5)-4 (12x3)
y' = -3( 3x4 - 5)-2
y' = 3( 3x4 - 5)-4 (12x3)
8
Find the derivative at the given value.
f'(3) = 45
f'(3) = -3
f'(3) = 4
f'(3) = 3
9
Find dy/dx .
y' = (-2x5)(5x4) + (x5 - 2)(-10x4)
y' = (-2x5)(5x4) - (x5 - 2)(-10x4)
y' = (-2x5)(5x4)(x5 - 2)(-10x4)
y' = -100x9 +20x4
10
Find f'(x).
f'(x) = [(5x4)(10x4) - (2x5 + 2)(20x3)] / (2x5 + 2)2
f'(x) = [(2x5 + 2)(20x3) - (5x4)(10x4)] / (2x5 + 2)
f'(x) = -(5x4)(2x5 + 2)-2(10x4) + (2x5 + 1)-1(20x3)
f'(x) = [(2x5 + 2)(20x3) - (5x4)(10x4)] / (2x5 + 2)2
11
Find dy/dx
y' = -12x3
y' = -4x4
y' = 12x3
y' = -3x3
12
Find the instantaneous rate of change of the function at the given value.
1
2
3
4
13
Uh-oh. Where is this function NOT differentiable?
At x = 0.
At x = 2.
At x = 1.
Nowhere! The graph is fine!
14
Find dy/dx.
y' = (1/2)(x2 + 1)(1/2) (2x)
y' = x(x2 + 1)(-1/2)
y' = (1/2)(x2 + 1)(-1/2)
y' = (1/2)(x2 + 1)(-1/2) (2x)
15
A derivative is also ________________
my worst nightmare.
the slope.
the instantaneous rate of change.
the instantaneous velocity.

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