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Popular >

derivative of f(x)=x^3-3x^2-45x+5

Solution

derivative of

f (x) = x^{3} - 3 x^{2} - 45 x + 5

Solution

3 x^{2} - 6 x - 45

Solution steps

\frac{d}{d x} (x^{3} - 3 x^{2} - 45 x + 5)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (3 x^{2}) - \frac{d}{d x} (45 x) + \frac{d}{d x} (5)

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (3 x^{2}) = 6 x

\frac{d}{d x} (45 x) = 45

\frac{d}{d x} (5) = 0

= 3 x^{2} - 6 x - 45 + 0

Simplify

= 3 x^{2} - 6 x - 45

Popular Examples

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y^{''}-3/t y^'+(20)/(t^2)y=0

y^{^{''}} - \frac{3}{t} y^{^{'}} + \frac{20}{t ^{2}} y = 0

derivative of arcsin(2x-3)derivative of

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\int \frac{x}{sec ( x )} d x

implicit (dy)/(dx),y^x=x^y implicit derivative

\frac{d y}{d x}, y^{x} = x^{y}

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^3-3x^2-45x+5 ?
The derivative of f(x)=x^3-3x^2-45x+5 is 3x^2-6x-45
What is the first derivative of f(x)=x^3-3x^2-45x+5 ?
The first derivative of f(x)=x^3-3x^2-45x+5 is 3x^2-6x-45