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

The derivative of f(x)=(2x-7)^4(x^2+x+1)^5 is 8(2x-7)^3(x^2+x+1)^5+5(x^2+x+1)^4(2x+1)(2x-7)^4

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

The first derivative of f(x)=(2x-7)^4(x^2+x+1)^5 is 8(2x-7)^3(x^2+x+1)^5+5(x^2+x+1)^4(2x+1)(2x-7)^4

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derivative of

f (x) = (2 x - 7)^{4} (x^{2} + x + 1)^{5}

8 (2 x - 7)^{3} (x^{2} + x + 1)^{5} + 5 (x^{2} + x + 1)^{4} (2 x + 1) (2 x - 7)^{4}

Solution steps

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

Apply the Product Rule:

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

f = (2 x - 7)^{4}, g = (x^{2} + x + 1)^{5}

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

\frac{d}{d x} ((2 x - 7)^{4}) = 8 (2 x - 7)^{3}

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

= 8 (2 x - 7)^{3} (x^{2} + x + 1)^{5} + 5 (x^{2} + x + 1)^{4} (2 x + 1) (2 x - 7)^{4}

\int \frac{1 + x ^{2}}{x ^{3}} d x

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

cos (\frac{x}{2})

\int \frac{1}{e ^{5 x}} d x

\int - 7 x^{- 8} d x

What is the derivative of f(x)=(2x-7)^4(x^2+x+1)^5 ?
The derivative of f(x)=(2x-7)^4(x^2+x+1)^5 is 8(2x-7)^3(x^2+x+1)^5+5(x^2+x+1)^4(2x+1)(2x-7)^4
What is the first derivative of f(x)=(2x-7)^4(x^2+x+1)^5 ?
The first derivative of f(x)=(2x-7)^4(x^2+x+1)^5 is 8(2x-7)^3(x^2+x+1)^5+5(x^2+x+1)^4(2x+1)(2x-7)^4