What is the derivative of f(x)=3x^2(x^3+1)^7 ?

The derivative of f(x)=3x^2(x^3+1)^7 is 3(2x(x^3+1)^7+21x^4(x^3+1)^6)

What is the first derivative of f(x)=3x^2(x^3+1)^7 ?

The first derivative of f(x)=3x^2(x^3+1)^7 is 3(2x(x^3+1)^7+21x^4(x^3+1)^6)

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derivative of

f (x) = 3 x^{2} (x^{3} + 1)^{7}

3 (2 x (x^{3} + 1)^{7} + 21 x^{4} (x^{3} + 1)^{6})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} ((x^{3} + 1)^{7}) = 21 x^{2} (x^{3} + 1)^{6}

= 3 (2 x (x^{3} + 1)^{7} + 21 x^{2} (x^{3} + 1)^{6} x^{2})

21 x^{2} (x^{3} + 1)^{6} x^{2} = 21 x^{4} (x^{3} + 1)^{6}

= 3 (2 x (x^{3} + 1)^{7} + 21 x^{4} (x^{3} + 1)^{6})

\frac{d y}{d x} = \frac{y - 1 - 2 y + y + 1}{x ^{2}}

y = \frac{- x ^{3}}{2} - \frac{x ^{2}}{2} + \frac{5 x}{2}, y = \frac{- x}{2}

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

x \to + 1 lim (ln (x))

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

What is the derivative of f(x)=3x^2(x^3+1)^7 ?
The derivative of f(x)=3x^2(x^3+1)^7 is 3(2x(x^3+1)^7+21x^4(x^3+1)^6)
What is the first derivative of f(x)=3x^2(x^3+1)^7 ?
The first derivative of f(x)=3x^2(x^3+1)^7 is 3(2x(x^3+1)^7+21x^4(x^3+1)^6)