What is the derivative of f(x)=13x^3(x^2-3) ?

The derivative of f(x)=13x^3(x^2-3) is 13(5x^4-9x^2)

What is the first derivative of f(x)=13x^3(x^2-3) ?

The first derivative of f(x)=13x^3(x^2-3) is 13(5x^4-9x^2)

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derivative of

f (x) = 13 x^{3} (x^{2} - 3)

13 (5 x^{4} - 9 x^{2})

Solution steps

\frac{d}{d x} (13 x^{3} (x^{2} - 3))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 13 \frac{d}{d x} (x^{3} (x^{2} - 3))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = x^{2} - 3

= 13 (\frac{d}{d x} (x^{3}) (x^{2} - 3) + \frac{d}{d x} (x^{2} - 3) x^{3})

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

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

= 13 (3 x^{2} (x^{2} - 3) + 2 x x^{3})

Simplify

13 (3 x^{2} (x^{2} - 3) + 2 x x^{3}) : 13 (5 x^{4} - 9 x^{2})

= 13 (5 x^{4} - 9 x^{2})

y = \frac{x}{81 + x ^{2}}, (0, 0)

\int \frac{14}{x ( x ^{2} + 25 )} d x

y^{^{''}} - 4 y^{^{'}} - 5 y = 0

x + y^{2} = 42, x = y

f (x) = x - 2, at x = 6

What is the derivative of f(x)=13x^3(x^2-3) ?
The derivative of f(x)=13x^3(x^2-3) is 13(5x^4-9x^2)
What is the first derivative of f(x)=13x^3(x^2-3) ?
The first derivative of f(x)=13x^3(x^2-3) is 13(5x^4-9x^2)