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Popular >

derivative of y^{3x}

Solution

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

Solution

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

Solution steps

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

Apply exponent rule:

a^{b} = e^{b l n (a)}

y^{3 x} = e^{3 x l n (y)}

= \frac{d}{d x} (e^{3 x l n (y)})

Apply the chain rule:

e^{3 x l n (y)} \frac{d}{d x} (3 x ln (y))

= e^{3 x l n (y)} \frac{d}{d x} (3 x ln (y))

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

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

e^{3 x l n (y)} = y^{3 x}

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

Popular Examples

integral of (x^2-3)^3(2x)

\int (x^{2} - 3)^{3} (2 x) d x

derivative of f(x)=7-5x^2 derivative of

f (x) = 7 - 5 x^{2}

integral of 3sqrt(x+1)

\int 3 x + 1 d x

tangent of f(x)=x^2-2,(5,23)tangent of

f (x) = x^{2} - 2, (5, 23)

inverse oflaplace (10*e^{-s})/(5s+1)inverse laplace

\frac{10 \cdot e ^{- s}}{5 s + 1}

Frequently Asked Questions (FAQ)

What is the derivative of y^{3x} ?
The derivative of y^{3x} is 3(ln(y)+(x(dy)/(dx))/y)y^{3x}
What is the first derivative of y^{3x} ?
The first derivative of y^{3x} is 3(ln(y)+(x(dy)/(dx))/y)y^{3x}