What is the derivative of (3x^4(2x^5)) ?

The derivative of (3x^4(2x^5)) is 54x^8

What is the first derivative of (3x^4(2x^5)) ?

The first derivative of (3x^4(2x^5)) is 54x^8

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\frac{d}{d x} ((3 x^{4}) (2 x^{5}))

54 x^{8}

Solution steps

\frac{d}{d x} ((3 x^{4}) (2 x^{5}))

Simplify

(3 x^{4}) (2 x^{5}) : 6 x^{9}

= \frac{d}{d x} (6 x^{9})

Take the constant out:

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

= 6 \frac{d}{d x} (x^{9})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 6 \cdot 9 x^{9 - 1}

Simplify

= 54 x^{8}

\int e^{3 x - 5} d x

\frac{d}{d x} (\frac{3 x + 1}{2 x - 5})

\int_{b}^{2 b} x^{4} d x

\frac{d}{d x} (x^{3} e^{- 3 x})

\frac{d}{d x} (5 e^{4 x} - cos^{2} (2 e^{x}))

What is the derivative of (3x^4(2x^5)) ?
The derivative of (3x^4(2x^5)) is 54x^8
What is the first derivative of (3x^4(2x^5)) ?
The first derivative of (3x^4(2x^5)) is 54x^8