What is the derivative of f(x)=n(n^2+3n-4)^7 ?

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

What is the first derivative of f(x)=n(n^2+3n-4)^7 ?

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

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derivative of

f (x) = n (n^{2} + 3 n - 4)^{7}

(n^{2} + 3 n - 4)^{7} + 7 n (n^{2} + 3 n - 4)^{6} (2 n + 3)

Solution steps

\frac{d}{d n} (n (n^{2} + 3 n - 4)^{7})

Apply the Product Rule:

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

f = n, g = (n^{2} + 3 n - 4)^{7}

= \frac{d n}{d n} (n^{2} + 3 n - 4)^{7} + \frac{d}{d n} ((n^{2} + 3 n - 4)^{7}) n

\frac{d n}{d n} = 1

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

= 1 \cdot (n^{2} + 3 n - 4)^{7} + 7 (n^{2} + 3 n - 4)^{6} (2 n + 3) n

Simplify

= (n^{2} + 3 n - 4)^{7} + 7 n (n^{2} + 3 n - 4)^{6} (2 n + 3)

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