Solved: "Find the derivatives y=(x5−2)(4x+3)3" - Plainmath

Harlen Pritchard

Answered question

2021-09-17

Find the derivatives

y = (x^{5} - 2) {(4 x + 3)}^{3}

Answer & Explanation

bahaistag

Skilled2021-09-18Added 100 answers

Step 1
The given function is

y = (x^{5} - 2) {(4 x + 3)}^{3}

differentiate with respect to x
Step 2

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

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

(using

\frac{d}{d x} u \cdot v = u \frac{d}{d x} v + v \frac{d}{d x} u

)

\frac{d y}{d x} = ((x^{5} - 2) \times 3 {(4 x + 3)}^{2} \frac{d}{d x} (4 x + 3) + {(4 x + 3)}^{3} (5 x^{4} - 0))

(using

\frac{d}{d x} x^{n} = n x^{n - 1}

)

\frac{d y}{d x} = ((x^{5} - 2) \times 3 {(4 x + 3)}^{2} \times 4 + {(4 x + 3)}^{3} (5 x^{4} - 0))

\frac{d y}{d x} = 12 (x^{5} - 2) {(4 x + 3)}^{2} + 5 x^{4} {(4 x + 3)}^{3}

(answer)

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