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

The derivative of f(x)=3x^5(x^3-2x) is 3(8x^7-12x^5)

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

The first derivative of f(x)=3x^5(x^3-2x) is 3(8x^7-12x^5)

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derivative of

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

3 (8 x^{7} - 12 x^{5})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{5}) = 5 x^{4}

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

= 3 (5 x^{4} (x^{3} - 2 x) + (3 x^{2} - 2) x^{5})

Expand

5 x^{4} (x^{3} - 2 x) + (3 x^{2} - 2) x^{5} : 8 x^{7} - 12 x^{5}

= 3 (8 x^{7} - 12 x^{5})

\int \frac{3}{2 9 - x ^{2}} d x

\int e^{3 x} + 1 d x

\int 12 x + 24 x^{2} d x

y^{^{'}} - y = e^{x} y^{2}

\frac{d}{d x} (\frac{x - 43}{x - 43})

What is the derivative of f(x)=3x^5(x^3-2x) ?
The derivative of f(x)=3x^5(x^3-2x) is 3(8x^7-12x^5)
What is the first derivative of f(x)=3x^5(x^3-2x) ?
The first derivative of f(x)=3x^5(x^3-2x) is 3(8x^7-12x^5)