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Popular >

derivative of (3x^2-3x+1)(x^3)

Solution

derivative of

(3 x^{2} - 3 x + 1) (x^{3})

Solution

15 x^{4} - 12 x^{3} + 3 x^{2}

Solution steps

\frac{d}{d x} ((3 x^{2} - 3 x + 1) x^{3})

Apply the Product Rule:

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

f = 3 x^{2} - 3 x + 1, g = x^{3}

= \frac{d}{d x} (3 x^{2} - 3 x + 1) x^{3} + \frac{d}{d x} (x^{3}) (3 x^{2} - 3 x + 1)

\frac{d}{d x} (3 x^{2} - 3 x + 1) = 6 x - 3

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

= (6 x - 3) x^{3} + 3 x^{2} (3 x^{2} - 3 x + 1)

Simplify

(6 x - 3) x^{3} + 3 x^{2} (3 x^{2} - 3 x + 1) : 15 x^{4} - 12 x^{3} + 3 x^{2}

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

Popular Examples

integral of 1/((4+x^2)^{5/2)}

\int \frac{1}{( 4 + x ^{2} ) ^{\frac{5}{2}}} d x

integral of ((5+ln(x))^5)/x

\int \frac{( 5 + ln ( x ) ) ^{5}}{x} d x

derivative of ln((x^3(2x+1)/(x^2-3)))

\frac{d}{d x} (ln (\frac{x ^{3} ( 2 x + 1 )}{x ^{2} - 3}))

derivative of f(x)=6cos^4(3x+2)derivative of

f (x) = 6 cos^{4} (3 x + 2)

limit as x approaches 5 of x^3-x^2+5x

x \to 5 lim (x^{3} - x^{2} + 5 x)

Frequently Asked Questions (FAQ)

What is the derivative of (3x^2-3x+1)(x^3) ?
The derivative of (3x^2-3x+1)(x^3) is 15x^4-12x^3+3x^2
What is the first derivative of (3x^2-3x+1)(x^3) ?
The first derivative of (3x^2-3x+1)(x^3) is 15x^4-12x^3+3x^2