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Popular >

derivative of 3^xsin^2(5x)

Solution

\frac{d}{d x} (3^{x} sin^{2} (5 x))

Solution

3^{x} ln (3) sin^{2} (5 x) + 5 sin (10 x) \cdot 3^{x}

Solution steps

\frac{d}{d x} (3^{x} sin^{2} (5 x))

Apply the Product Rule:

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

f = 3^{x}, g = sin^{2} (5 x)

= \frac{d}{d x} (3^{x}) sin^{2} (5 x) + \frac{d}{d x} (sin^{2} (5 x)) 3^{x}

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

\frac{d}{d x} (sin^{2} (5 x)) = 5 sin (10 x)

= 3^{x} ln (3) sin^{2} (5 x) + 5 sin (10 x) \cdot 3^{x}

Popular Examples

(\partial)/(\partial x)(8+xln(xy-9))

\frac{\partial}{\partial x} (8 + x ln (x y - 9))

(\partial)/(\partial x)(xcos(x+y)+y)

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

integral from-2 to 0 of (x-2)(x+1)

\int_{- 2}^{0} (x - 2) (x + 1) d x

area y=8x,y= 5/2 x,y=9-x^2 area

y = 8 x, y = \frac{5}{2} x, y = 9 - x^{2}

limit as x approaches 4-of 4-x

x \to 4 - lim (4 - x)

Frequently Asked Questions (FAQ)

What is the derivative of 3^xsin^2(5x) ?
The derivative of 3^xsin^2(5x) is 3^xln(3)sin^2(5x)+5sin(10x)*3^x
What is the first derivative of 3^xsin^2(5x) ?
The first derivative of 3^xsin^2(5x) is 3^xln(3)sin^2(5x)+5sin(10x)*3^x