What is the derivative of (6x^5-4x^4+7x(x^3-x^2-1)) ?

The derivative of (6x^5-4x^4+7x(x^3-x^2-1)) is 48x^7-70x^6+24x^5-30x^4+44x^3-21x^2-7

What is the first derivative of (6x^5-4x^4+7x(x^3-x^2-1)) ?

The first derivative of (6x^5-4x^4+7x(x^3-x^2-1)) is 48x^7-70x^6+24x^5-30x^4+44x^3-21x^2-7

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\frac{d}{d x} ((6 x^{5} - 4 x^{4} + 7 x) (x^{3} - x^{2} - 1))

48 x^{7} - 70 x^{6} + 24 x^{5} - 30 x^{4} + 44 x^{3} - 21 x^{2} - 7

Solution steps

\frac{d}{d x} ((6 x^{5} - 4 x^{4} + 7 x) (x^{3} - x^{2} - 1))

Apply the Product Rule:

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

f = 6 x^{5} - 4 x^{4} + 7 x, g = x^{3} - x^{2} - 1

= \frac{d}{d x} (6 x^{5} - 4 x^{4} + 7 x) (x^{3} - x^{2} - 1) + \frac{d}{d x} (x^{3} - x^{2} - 1) (6 x^{5} - 4 x^{4} + 7 x)

\frac{d}{d x} (6 x^{5} - 4 x^{4} + 7 x) = 30 x^{4} - 16 x^{3} + 7

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

= (30 x^{4} - 16 x^{3} + 7) (x^{3} - x^{2} - 1) + (3 x^{2} - 2 x) (6 x^{5} - 4 x^{4} + 7 x)

Simplify

(30 x^{4} - 16 x^{3} + 7) (x^{3} - x^{2} - 1) + (3 x^{2} - 2 x) (6 x^{5} - 4 x^{4} + 7 x) : 48 x^{7} - 70 x^{6} + 24 x^{5} - 30 x^{4} + 44 x^{3} - 21 x^{2} - 7

= 48 x^{7} - 70 x^{6} + 24 x^{5} - 30 x^{4} + 44 x^{3} - 21 x^{2} - 7

\frac{\partial}{\partial x} (e^{x + y + 5})

\frac{\partial}{\partial z} (\frac{x - y}{x + z})

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{t}}{1 + t ^{2}}

\int_{0}^{π} sin^{4} (3 x) d x

\int - 1 d x

What is the derivative of (6x^5-4x^4+7x(x^3-x^2-1)) ?
The derivative of (6x^5-4x^4+7x(x^3-x^2-1)) is 48x^7-70x^6+24x^5-30x^4+44x^3-21x^2-7
What is the first derivative of (6x^5-4x^4+7x(x^3-x^2-1)) ?
The first derivative of (6x^5-4x^4+7x(x^3-x^2-1)) is 48x^7-70x^6+24x^5-30x^4+44x^3-21x^2-7