Solved: "Write formulas for the indicated partial derivatives for..."

cistG

Answered question

2020-11-23

Write formulas for the indicated partial derivatives for the multivariable function.

k (a, b) = 3 a b^{4} + 8 ({1.4}^{b})

\frac{\partial k}{\partial a}

\frac{\partial k}{\partial b}

\frac{\partial k}{\partial b} ∣_{a = 3}

Answer & Explanation

Latisha Oneil

Skilled2020-11-24Added 100 answers

\frac{\partial k}{\partial a} = \frac{\partial}{\partial a} [3 a b^{4} + 8 ({1.4}^{b})]

\frac{\partial k}{\partial a} = 3 b^{4} + 0 = 3 b^{4}

\frac{\partial k}{\partial a} = 3 b^{4}

\frac{\partial k}{\partial b} = \frac{\partial}{\partial b} [3 a b^{4} + 8 ({1.4}^{b})]

\frac{\partial k}{\partial b} = 3 a \cdot 4 b^{9} + 8 ({1.4}^{b}) \log (1 \cdot 4)

\frac{\partial k}{\partial b} = 12 a b^{3} + 8 \ln (1.4) ({1.4}^{b})

\frac{\partial k}{\partial b} ∣_{a = 3} = 12 \cdot 3 b^{3} + 8 \ln (1.4) ({1.4}^{b})

\frac{\partial k}{\partial b} ∣_{a = 3} = 36 b^{3} + 8 \ln (1.4) ({1.4}^{b})

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