What is the derivative of sin(t^2)*ln(t^3) ?

The derivative of sin(t^2)*ln(t^3) is 2tcos(t^2)ln(t^3)+(3sin(t^2))/t

What is the first derivative of sin(t^2)*ln(t^3) ?

The first derivative of sin(t^2)*ln(t^3) is 2tcos(t^2)ln(t^3)+(3sin(t^2))/t

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derivative of

sin (t^{2}) \cdot ln (t^{3})

2 t cos (t^{2}) ln (t^{3}) + \frac{3 sin ( t ^{2} )}{t}

Solution steps

\frac{d}{d t} (sin (t^{2}) ln (t^{3}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (t^{2}), g = ln (t^{3})

= \frac{d}{d t} (sin (t^{2})) ln (t^{3}) + \frac{d}{d t} (ln (t^{3})) sin (t^{2})

\frac{d}{d t} (sin (t^{2})) = cos (t^{2}) \cdot 2 t

\frac{d}{d t} (ln (t^{3})) = \frac{3}{t}

= cos (t^{2}) \cdot 2 t ln (t^{3}) + \frac{3}{t} sin (t^{2})

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= 2 t cos (t^{2}) ln (t^{3}) + \frac{3 sin ( t ^{2} )}{t}

\frac{\partial}{\partial x} ((1 + \frac{2}{y}) sin (x))

\frac{\partial}{\partial y} ((\frac{x}{y})^{\frac{1}{2}})

\frac{d}{d x} (2 x z (x))

\frac{d}{d s} (\frac{s}{s ^{2} + 9})

\int \frac{1}{x ( x - 1 ) ^{3}} d x

What is the derivative of sin(t^2)*ln(t^3) ?
The derivative of sin(t^2)*ln(t^3) is 2tcos(t^2)ln(t^3)+(3sin(t^2))/t
What is the first derivative of sin(t^2)*ln(t^3) ?
The first derivative of sin(t^2)*ln(t^3) is 2tcos(t^2)ln(t^3)+(3sin(t^2))/t