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Popular >

derivative of y^5sin(5x)

Solution

\frac{d}{d x} (y^{5} sin (5 x))

Solution

5 y^{4} \frac{d y}{d x} sin (5 x) + cos (5 x) \cdot 5 y^{5}

Solution steps

\frac{d}{d x} (y^{5} sin (5 x))

Apply the Product Rule:

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

f = y^{5}, g = sin (5 x)

= \frac{d}{d x} (y^{5}) sin (5 x) + \frac{d}{d x} (sin (5 x)) y^{5}

\frac{d}{d x} (y^{5}) = 5 y^{4} \frac{d y}{d x}

\frac{d}{d x} (sin (5 x)) = cos (5 x) \cdot 5

= 5 y^{4} \frac{d y}{d x} sin (5 x) + cos (5 x) \cdot 5 y^{5}

Popular Examples

(\partial)/(\partial x)(4sin(4x)e^{3x})

\frac{\partial}{\partial x} (4 sin (4 x) e^{3 x})

sum from n=1 to infinity of 5/(4^{n-1)}

n = 1 \sum \infty \frac{5}{4 ^{n - 1}}

(\partial)/(\partial y)(e^{x^2+y^2})

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

sum from k=1 to infinity of e^{-k}

k = 1 \sum \infty e^{- k}

(\partial)/(\partial x)(4xyarcsin(yz))

\frac{\partial}{\partial x} (4 x y arcsin (yz))

Frequently Asked Questions (FAQ)

What is the derivative of y^5sin(5x) ?
The derivative of y^5sin(5x) is 5y^4(dy)/(dx)sin(5x)+cos(5x)*5y^5
What is the first derivative of y^5sin(5x) ?
The first derivative of y^5sin(5x) is 5y^4(dy)/(dx)sin(5x)+cos(5x)*5y^5