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Popular >

derivative of xln(y+sin(3x))

Solution

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

Solution

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{d}{d x} (sin (3 x)) = cos (3 x) \cdot 3

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

Popular Examples

sum from n=1 to infinity of (10/17)^n

n = 1 \sum \infty (\frac{10}{17})^{n}

(\partial)/(\partial x)(cos(xy)y)

\frac{\partial}{\partial x} (cos (x y) y)

derivative of sin^{cos(x}(x))

\frac{d}{d x} (sin^{c o s (x)} (x))

integral of (2e^{2t})/(5+e^{2t)}

\int \frac{2 e ^{2 t}}{5 + e ^{2 t}} d t

derivative of 64x^2 derivative of

64 x^{2}

Frequently Asked Questions (FAQ)

What is the derivative of xln(y+sin(3x)) ?
The derivative of xln(y+sin(3x)) is ln(y)+(x(dy)/(dx))/y+cos(3x)*3
What is the first derivative of xln(y+sin(3x)) ?
The first derivative of xln(y+sin(3x)) is ln(y)+(x(dy)/(dx))/y+cos(3x)*3