What is the derivative of (7x^2+6x^7(3x-1)^4) ?

The derivative of (7x^2+6x^7(3x-1)^4) is 7(7x^2+6x)^6(14x+6)(3x-1)^4+12(3x-1)^3(7x^2+6x)^7

What is the first derivative of (7x^2+6x^7(3x-1)^4) ?

The first derivative of (7x^2+6x^7(3x-1)^4) is 7(7x^2+6x)^6(14x+6)(3x-1)^4+12(3x-1)^3(7x^2+6x)^7

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\frac{d}{d x} ((7 x^{2} + 6 x)^{7} (3 x - 1)^{4})

7 (7 x^{2} + 6 x)^{6} (14 x + 6) (3 x - 1)^{4} + 12 (3 x - 1)^{3} (7 x^{2} + 6 x)^{7}

Solution steps

\frac{d}{d x} ((7 x^{2} + 6 x)^{7} (3 x - 1)^{4})

Apply the Product Rule:

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

f = (7 x^{2} + 6 x)^{7}, g = (3 x - 1)^{4}

= \frac{d}{d x} ((7 x^{2} + 6 x)^{7}) (3 x - 1)^{4} + \frac{d}{d x} ((3 x - 1)^{4}) (7 x^{2} + 6 x)^{7}

\frac{d}{d x} ((7 x^{2} + 6 x)^{7}) = 7 (7 x^{2} + 6 x)^{6} (14 x + 6)

\frac{d}{d x} ((3 x - 1)^{4}) = 12 (3 x - 1)^{3}

= 7 (7 x^{2} + 6 x)^{6} (14 x + 6) (3 x - 1)^{4} + 12 (3 x - 1)^{3} (7 x^{2} + 6 x)^{7}

\frac{\partial}{\partial x} (x^{3} + y^{3} + x y)

\int \frac{7 sin ( 2 x )}{1 + cos ^{4} ( x )} d x

\frac{d}{d x} ((x^{11} - 2)^{3})

x^{2} (x^{3} + 5)^{3}

What is the derivative of (7x^2+6x^7(3x-1)^4) ?
The derivative of (7x^2+6x^7(3x-1)^4) is 7(7x^2+6x)^6(14x+6)(3x-1)^4+12(3x-1)^3(7x^2+6x)^7
What is the first derivative of (7x^2+6x^7(3x-1)^4) ?
The first derivative of (7x^2+6x^7(3x-1)^4) is 7(7x^2+6x)^6(14x+6)(3x-1)^4+12(3x-1)^3(7x^2+6x)^7