What is the derivative of (15x^7+27x^5/(3x)) ?

The derivative of (15x^7+27x^5/(3x)) is 30x^5+36x^3

What is the first derivative of (15x^7+27x^5/(3x)) ?

The first derivative of (15x^7+27x^5/(3x)) is 30x^5+36x^3

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\frac{d}{d x} (\frac{15 x ^{7} + 27 x ^{5}}{3 x})

30 x^{5} + 36 x^{3}

Solution steps

\frac{d}{d x} (\frac{15 x ^{7} + 27 x ^{5}}{3 x})

Simplify

\frac{15 x ^{7} + 27 x ^{5}}{3 x} : x^{4} (5 x^{2} + 9)

= \frac{d}{d x} (x^{4} (5 x^{2} + 9))

Apply the Product Rule:

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

f = x^{4}, g = 5 x^{2} + 9

= \frac{d}{d x} (x^{4}) (5 x^{2} + 9) + \frac{d}{d x} (5 x^{2} + 9) x^{4}

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

\frac{d}{d x} (5 x^{2} + 9) = 10 x

= 4 x^{3} (5 x^{2} + 9) + 10 x x^{4}

Simplify

4 x^{3} (5 x^{2} + 9) + 10 x x^{4} : 30 x^{5} + 36 x^{3}

= 30 x^{5} + 36 x^{3}

y = x^{3 x}

x^{2} + y^{2}

x \frac{d y}{d x} - 3 y = 7 x^{4}, y (1) = 2

f (x) = \frac{x}{x - 3}

\int ln (x^{2} - x - 6) d x

What is the derivative of (15x^7+27x^5/(3x)) ?
The derivative of (15x^7+27x^5/(3x)) is 30x^5+36x^3
What is the first derivative of (15x^7+27x^5/(3x)) ?
The first derivative of (15x^7+27x^5/(3x)) is 30x^5+36x^3