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

The derivative of f(x)=3x^3(x^2-3x+5) is 3(5x^4-12x^3+15x^2)

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

The first derivative of f(x)=3x^3(x^2-3x+5) is 3(5x^4-12x^3+15x^2)

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derivative of

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

3 (5 x^{4} - 12 x^{3} + 15 x^{2})

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Expand

3 x^{2} (x^{2} - 3 x + 5) + (2 x - 3) x^{3} : 5 x^{4} - 12 x^{3} + 15 x^{2}

= 3 (5 x^{4} - 12 x^{3} + 15 x^{2})

\frac{d}{d x} (sin (3 x) + cos (4 x))

\frac{d}{d t} (r (t) cos (t))

3 x y d y = (y^{2} - x^{2}) d x

\int \frac{4}{x} - \frac{16}{x ^{2}} d x

What is the derivative of f(x)=3x^3(x^2-3x+5) ?
The derivative of f(x)=3x^3(x^2-3x+5) is 3(5x^4-12x^3+15x^2)
What is the first derivative of f(x)=3x^3(x^2-3x+5) ?
The first derivative of f(x)=3x^3(x^2-3x+5) is 3(5x^4-12x^3+15x^2)