What is the derivative of (3x+1^6sqrt(2x-5)) ?

The derivative of (3x+1^6sqrt(2x-5)) is 18(3x+1)^5sqrt(2x-5)+((3x+1)^6)/(sqrt(2x-5))

What is the first derivative of (3x+1^6sqrt(2x-5)) ?

The first derivative of (3x+1^6sqrt(2x-5)) is 18(3x+1)^5sqrt(2x-5)+((3x+1)^6)/(sqrt(2x-5))

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\frac{d}{d x} ((3 x + 1)^{6} 2 x - 5)

18 (3 x + 1)^{5} 2 x - 5 + \frac{( 3 x + 1 ) ^{6}}{2 x - 5}

Solution steps

\frac{d}{d x} ((3 x + 1)^{6} 2 x - 5)

Apply the Product Rule:

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

f = (3 x + 1)^{6}, g = 2 x - 5

= \frac{d}{d x} ((3 x + 1)^{6}) 2 x - 5 + \frac{d}{d x} (2 x - 5) (3 x + 1)^{6}

\frac{d}{d x} ((3 x + 1)^{6}) = 18 (3 x + 1)^{5}

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

= 18 (3 x + 1)^{5} 2 x - 5 + \frac{1}{2 x - 5} (3 x + 1)^{6}

\frac{1}{2 x - 5} (3 x + 1)^{6} = \frac{( 3 x + 1 ) ^{6}}{2 x - 5}

= 18 (3 x + 1)^{5} 2 x - 5 + \frac{( 3 x + 1 ) ^{6}}{2 x - 5}

\int 2 x d x

\frac{d}{d r} (r^{3})

f (x) = arctan (4 x)

\int (5 x^{3} - 2 x^{2} + 3) d x

x \to 0 lim (\frac{e ^{x} - 1}{6 x})

What is the derivative of (3x+1^6sqrt(2x-5)) ?
The derivative of (3x+1^6sqrt(2x-5)) is 18(3x+1)^5sqrt(2x-5)+((3x+1)^6)/(sqrt(2x-5))
What is the first derivative of (3x+1^6sqrt(2x-5)) ?
The first derivative of (3x+1^6sqrt(2x-5)) is 18(3x+1)^5sqrt(2x-5)+((3x+1)^6)/(sqrt(2x-5))