Step by step solution to "Find the derivative of y=3ax(x2−3x+1)." - Plainmath

Cordazzoyn

Answered question

2021-11-17

Find the derivative of

y = 3 a^{x} (x^{2} - 3 x + 1)

.

Answer & Explanation

Forneadil

Beginner2021-11-18Added 18 answers

Step 1
Given function is:

y = 3 a^{x} (x^{2} - 3 x + 1)

We have to find the derivative dy/dx.
We will use the following formula for derivatives:
Given: y=f(x)g(x)

\frac{d y}{d x} = f^{'} (x) g (x) + f (x) g^{'} (x)

Step 2
Here in our problem,

f (x) = 3 a^{x}

g (x) = x^{2} - 3 x + 1

Then we get,

\frac{d y}{d x} = 3 a^{x} \ln (a) \cdot (x^{2} - 3 x + 1) + 3 a^{x} (2 x - 3)

\frac{d y}{d x} = 3 a^{x} [x^{2} \ln (a) + (2 - 3 \ln (a)) x + \ln (a) - 3]

Hence the answer.

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