What is the derivative of (4pix+3x^6/(sqrt(x))) ?

The derivative of (4pix+3x^6/(sqrt(x))) is (4pi+33x^5)/(2sqrt(x))

What is the first derivative of (4pix+3x^6/(sqrt(x))) ?

The first derivative of (4pix+3x^6/(sqrt(x))) is (4pi+33x^5)/(2sqrt(x))

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\frac{d}{d x} (\frac{4 π x + 3 x ^{6}}{x})

\frac{4 π + 33 x ^{5}}{2 x}

Solution steps

\frac{d}{d x} (\frac{4 π x + 3 x ^{6}}{x})

Simplify

\frac{4 π x + 3 x ^{6}}{x} : x (4 π + 3 x^{5})

= \frac{d}{d x} (x (4 π + 3 x^{5}))

Apply the Product Rule:

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

f = x, g = 4 π + 3 x^{5}

= \frac{d}{d x} (x) (4 π + 3 x^{5}) + \frac{d}{d x} (4 π + 3 x^{5}) x

\frac{d}{d x} (x) = \frac{1}{2 x}

\frac{d}{d x} (4 π + 3 x^{5}) = 15 x^{4}

= \frac{1}{2 x} (4 π + 3 x^{5}) + 15 x^{4} x

Simplify

\frac{1}{2 x} (4 π + 3 x^{5}) + 15 x^{4} x : \frac{4 π + 33 x ^{5}}{2 x}

= \frac{4 π + 33 x ^{5}}{2 x}

What is the derivative of (4pix+3x^6/(sqrt(x))) ?
The derivative of (4pix+3x^6/(sqrt(x))) is (4pi+33x^5)/(2sqrt(x))
What is the first derivative of (4pix+3x^6/(sqrt(x))) ?
The first derivative of (4pix+3x^6/(sqrt(x))) is (4pi+33x^5)/(2sqrt(x))