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Popular >

derivative of sin(xsin(3x))

Solution

\frac{d}{d x} (sin (x) sin (3 x))

Solution

cos (x) sin (3 x) + cos (3 x) \cdot 3 sin (x)

Solution steps

\frac{d}{d x} (sin (x) sin (3 x))

Apply the Product Rule:

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

f = sin (x), g = sin (3 x)

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

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

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

= cos (x) sin (3 x) + cos (3 x) \cdot 3 sin (x)

Popular Examples

tangent of 4x^2-2x+4 tangent of

4 x^{2} - 2 x + 4

(\partial)/(\partial x)(3x^2+6xy^3)

\frac{\partial}{\partial x} (3 x^{2} + 6 x y^{3})

laplacetransform 7-4t laplace transform

7 - 4 t

integral from 0 to 1 of 46 1/(x^p)

\int_{0}^{1} 46 \frac{1}{x ^{p}} d x

integral of 1/((1+4x^2)^{3/2)}

\int \frac{1}{( 1 + 4 x ^{2} ) ^{\frac{3}{2}}} d x

Frequently Asked Questions (FAQ)

What is the derivative of sin(xsin(3x)) ?
The derivative of sin(xsin(3x)) is cos(x)sin(3x)+cos(3x)*3sin(x)
What is the first derivative of sin(xsin(3x)) ?
The first derivative of sin(xsin(3x)) is cos(x)sin(3x)+cos(3x)*3sin(x)