What is the use of derivative function?

To calculate the tangent slope of a curve in different places

What is the derivative for dy/dx=√x?

f'\left(x\right)=\frac{1}{2\sqrt{x}}

What is the derivative forf\left(x\right)=x^{-1} ?

f'\left(x\right)=-\frac{1}{x^2}

What is the derivative for y= 6/∛x ?

f'\left(x\right)=-\frac{2}{x\sqrt[3]{x}}

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Math Derivatives Calculus

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Questions 14

Answers

1
What is the differentiation off\left(x\right)=x^7
f '(x)= 7x6
dy/dx= 7x8
f '(x)= 6x7
f '(x)= 7x7
2
What is the use of derivative function?
To find the slope of secant line.
To calculate the tangent slope of a curve in different places
To calculate limit of a function
To Calculate the best fit line in a scatter graph
3
What is the answer to \frac{d}{dx}x^{-4}
f'\left(x\right)=-4x^5
\frac{dy}{dx}=-4x^3
\frac{dy}{dx}=-5x^{-3}
\frac{dy}{dx}=-4x^{-5}
4
What is the derivative for y = 1 + 1/x ?
y' = -2/x2
y '= 1/x2
y '= -1/x2
y '= x-2
5
What are the ways to name the derivative?
f (x), dy/dx, y'
f '(x), dy/dx, y'
f '(y), dy/dx, y'
f '(x), dx/dy, y '
6
What is the derivative for y= 3x²+x-3 ?
f '(x)= 6x + 1
f '(x)= 6x2 + 1
f '(x)= 6x-2 + 1
f '(x)= 6x + 3
7
What is the derivative for dy/dx= x³-4x²?
f '(x)= 3x2 -8x
f '(x)= 3x3 -8x
f '(x)= 3x2 -16x
f ' (x)= 3x2 +8x
8
What is the derivative for f (x)=5x²?
dx/dy = 10x
f'(x)= 10x
y '= 10x2
y= 10x2
9
What is the power rule for \frac{d}{dx}\left(kx^n\right)?
f\left(x\right)=knx^{n-1}
f'\left(x\right)=-knx^{n-1}
f\left(x\right)=kx^{n-1}
f'\left(x\right)=nx^{n-1}
10
What is the derivative for dy/dx=√x?
f'\left(x\right)=-\frac{1}{2x^{-\frac{1}{2}}}
f'\left(x\right)=\frac{1}{2\sqrt{x}}
f'\left(x\right)=\frac{1}{2}\sqrt{x}
f'\left(x\right)=-\frac{1}{2\sqrt{x}}
11
What is the derivative forf\left(x\right)=x^{-1} ?
\frac{dy}{dx}=\frac{1}{^{x^2}}
f'\left(x\right)=-\frac{1}{x^2}
f'\left(x\right)=\frac{-2}{x^2}
f'\left(x\right)=-\frac{1}{x^{-2}}
12
What is the second derivative for y= x² + 1/x?
y ''=2 x-1/x2
y'' = 2+1/x3
y ''= 2+2/x3
y ''=2- 1/x2
13
What is the derivative for y= 6/∛x ?
f\left(x\right)=-\frac{1}{2x\sqrt[3]{x}}
f'\left(x\right)=-\frac{2}{\sqrt[3]{x^2}}
f'\left(x\right)=-\frac{2}{x\sqrt[3]{x}}
f'\left(x\right)=18x^{\frac{4}{3}}
14
What is the derivative for y= 3/x²?
y'= -6x3
y'= 6x-3
y'= -6x-3
y=3/2 x-3

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