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

The derivative of (3x+5)^4sqrt(x) is 12sqrt(x)(3x+5)^3+((3x+5)^4)/(2sqrt(x))

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

The first derivative of (3x+5)^4sqrt(x) is 12sqrt(x)(3x+5)^3+((3x+5)^4)/(2sqrt(x))

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derivative of

(3 x + 5)^{4} x

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

Solution steps

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

Apply the Product Rule:

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

f = (3 x + 5)^{4}, g = x

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

\frac{d}{d x} ((3 x + 5)^{4}) = 12 (3 x + 5)^{3}

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

= 12 (3 x + 5)^{3} x + \frac{1}{2 x} (3 x + 5)^{4}

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

= 12 x (3 x + 5)^{3} + \frac{( 3 x + 5 ) ^{4}}{2 x}

\int t e^{- 2} d t

y = - 4 x^{7} - 1

\int (cos (x) - sin (x)) d x

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

\frac{\partial}{\partial x} (\frac{9 x ^{2}}{( x - y ) ^{2}})

What is the derivative of (3x+5)^4sqrt(x) ?
The derivative of (3x+5)^4sqrt(x) is 12sqrt(x)(3x+5)^3+((3x+5)^4)/(2sqrt(x))
What is the first derivative of (3x+5)^4sqrt(x) ?
The first derivative of (3x+5)^4sqrt(x) is 12sqrt(x)(3x+5)^3+((3x+5)^4)/(2sqrt(x))