What is the derivative of 13x^3(x^2-5) ?

The derivative of 13x^3(x^2-5) is 13(5x^4-15x^2)

What is the first derivative of 13x^3(x^2-5) ?

The first derivative of 13x^3(x^2-5) is 13(5x^4-15x^2)

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derivative of

13 x^{3} (x^{2} - 5)

13 (5 x^{4} - 15 x^{2})

Solution steps

\frac{d}{d x} (13 x^{3} (x^{2} - 5))

Take the constant out:

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

= 13 \frac{d}{d x} (x^{3} (x^{2} - 5))

Apply the Product Rule:

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

f = x^{3}, g = x^{2} - 5

= 13 (\frac{d}{d x} (x^{3}) (x^{2} - 5) + \frac{d}{d x} (x^{2} - 5) x^{3})

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

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

= 13 (3 x^{2} (x^{2} - 5) + 2 x x^{3})

Simplify

13 (3 x^{2} (x^{2} - 5) + 2 x x^{3}) : 13 (5 x^{4} - 15 x^{2})

= 13 (5 x^{4} - 15 x^{2})

\frac{d}{d x} (arctan (\frac{0.9}{x}))

\frac{42}{x}

x \to - 2 lim (3 x + 8)

y = e^{- x^{9}}

\int \frac{cos ( 2 x )}{cos ^{2} ( x )} d x

What is the derivative of 13x^3(x^2-5) ?
The derivative of 13x^3(x^2-5) is 13(5x^4-15x^2)
What is the first derivative of 13x^3(x^2-5) ?
The first derivative of 13x^3(x^2-5) is 13(5x^4-15x^2)