What is (d^2)/(dx^2)((y)(3^x)) ?

The answer to (d^2)/(dx^2)((y)(3^x)) is ln^2(3)*3^xy+2ln(3)*3^x(dy)/(dx)+3^x(d^2y)/(dx^2)

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(d^2)/(dx^2)((y)(3^x))

\frac{d ^{2}}{d x ^{2}} ((y) (3^{x}))

ln^{2} (3) \cdot 3^{x} y + 2 ln (3) \cdot 3^{x} \frac{d y}{d x} + 3^{x} \frac{d ^{2} y}{d x ^{2}}

Solution steps

\frac{d ^{2}}{d x ^{2}} ((y) (3^{x}))

\frac{d}{d x} (y \cdot 3^{x}) = \frac{d y}{d x} 3^{x} + 3^{x} ln (3) y

= \frac{d}{d x} (\frac{d y}{d x} 3^{x} + 3^{x} ln (3) y)

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

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

5 x y + yz - 15 x - 3 z

- 2 k t + s^{{3}}

x^{2} - \frac{7}{3} x - 2

(\frac{3}{2})!

(x + Δ x)^{2}

What is (d^2)/(dx^2)((y)(3^x)) ?
The answer to (d^2)/(dx^2)((y)(3^x)) is ln^2(3)*3^xy+2ln(3)*3^x(dy)/(dx)+3^x(d^2y)/(dx^2)