What is the derivative of (6x^2+7(6x+sqrt(x))) ?

The derivative of (6x^2+7(6x+sqrt(x))) is 108x^2+12xsqrt(x)+3x^{3/2}+7/(2sqrt(x))+42

What is the first derivative of (6x^2+7(6x+sqrt(x))) ?

The first derivative of (6x^2+7(6x+sqrt(x))) is 108x^2+12xsqrt(x)+3x^{3/2}+7/(2sqrt(x))+42

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\frac{d}{d x} ((6 x^{2} + 7) (6 x + x))

108 x^{2} + 12 x x + 3 x^{\frac{3}{2}} + \frac{7}{2 x} + 42

Solution steps

\frac{d}{d x} ((6 x^{2} + 7) (6 x + x))

Apply the Product Rule:

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

f = 6 x^{2} + 7, g = 6 x + x

= \frac{d}{d x} (6 x^{2} + 7) (6 x + x) + \frac{d}{d x} (6 x + x) (6 x^{2} + 7)

\frac{d}{d x} (6 x^{2} + 7) = 12 x

\frac{d}{d x} (6 x + x) = 6 + \frac{1}{2 x}

= 12 x (6 x + x) + (6 + \frac{1}{2 x}) (6 x^{2} + 7)

Simplify

12 x (6 x + x) + (6 + \frac{1}{2 x}) (6 x^{2} + 7) : 108 x^{2} + 12 x x + 3 x^{\frac{3}{2}} + \frac{7}{2 x} + 42

= 108 x^{2} + 12 x x + 3 x^{\frac{3}{2}} + \frac{7}{2 x} + 42

0 = (x + y) d x + (x - y) d y

y^{^{''}} + y = 3 sec^{3} (2 t)

x = y^{2} - 4, x = 4

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

\int e^{x} sin (n x) d x

What is the derivative of (6x^2+7(6x+sqrt(x))) ?
The derivative of (6x^2+7(6x+sqrt(x))) is 108x^2+12xsqrt(x)+3x^{3/2}+7/(2sqrt(x))+42
What is the first derivative of (6x^2+7(6x+sqrt(x))) ?
The first derivative of (6x^2+7(6x+sqrt(x))) is 108x^2+12xsqrt(x)+3x^{3/2}+7/(2sqrt(x))+42