What is the derivative of (x^2+x^3*(3x^4-x^3)) ?

The derivative of (x^2+x^3*(3x^4-x^3)) is 21x^6+12x^5-5x^4

What is the first derivative of (x^2+x^3*(3x^4-x^3)) ?

The first derivative of (x^2+x^3*(3x^4-x^3)) is 21x^6+12x^5-5x^4

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\frac{d}{d x} ((x^{2} + x^{3}) \cdot (3 x^{4} - x^{3}))

21 x^{6} + 12 x^{5} - 5 x^{4}

Solution steps

\frac{d}{d x} ((x^{2} + x^{3}) (3 x^{4} - x^{3}))

Apply the Product Rule:

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

f = x^{2} + x^{3}, g = 3 x^{4} - x^{3}

= \frac{d}{d x} (x^{2} + x^{3}) (3 x^{4} - x^{3}) + \frac{d}{d x} (3 x^{4} - x^{3}) (x^{2} + x^{3})

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

\frac{d}{d x} (3 x^{4} - x^{3}) = 12 x^{3} - 3 x^{2}

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

Simplify

(2 x + 3 x^{2}) (3 x^{4} - x^{3}) + (12 x^{3} - 3 x^{2}) (x^{2} + x^{3}) : 21 x^{6} + 12 x^{5} - 5 x^{4}

= 21 x^{6} + 12 x^{5} - 5 x^{4}

What is the derivative of (x^2+x^3*(3x^4-x^3)) ?
The derivative of (x^2+x^3*(3x^4-x^3)) is 21x^6+12x^5-5x^4
What is the first derivative of (x^2+x^3*(3x^4-x^3)) ?
The first derivative of (x^2+x^3*(3x^4-x^3)) is 21x^6+12x^5-5x^4