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Popular >

derivative of f(x)=x^2sin(x^2+3)

Solution

derivative of

f (x) = x^{2} sin (x^{2} + 3)

Solution

2 x sin (x^{2} + 3) + 2 x^{3} cos (x^{2} + 3)

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

= 2 x sin (x^{2} + 3) + cos (x^{2} + 3) \cdot 2 x x^{2}

cos (x^{2} + 3) \cdot 2 x x^{2} = 2 x^{3} cos (x^{2} + 3)

= 2 x sin (x^{2} + 3) + 2 x^{3} cos (x^{2} + 3)

Popular Examples

derivative of g(t)=tsqrt(t)\sqrt[3]{t}derivative of

((7y^2-t^2)/(y^5))(dy)/(dt)+t/(2y^4)=0

(\frac{7 y ^{2} - t ^{2}}{y ^{5}}) \frac{d y}{d t} + \frac{t}{2 y ^{4}} = 0

integral of (sqrt(x^2-9))/(x^2)

\int \frac{x ^{2} - 9}{x ^{2}} d x

y^{''}-(6/x)y^'-(4/(x^2))y=0

y^{^{''}} - (\frac{6}{x}) y^{^{'}} - (\frac{4}{x ^{2}}) y = 0

d/(da)((pi(9a^2+6a+1))/(36a))

\frac{d}{d a} (\frac{π ( 9 a ^{2} + 6 a + 1 )}{36 a})

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=x^2sin(x^2+3) ?
The derivative of f(x)=x^2sin(x^2+3) is 2xsin(x^2+3)+2x^3cos(x^2+3)
What is the first derivative of f(x)=x^2sin(x^2+3) ?
The first derivative of f(x)=x^2sin(x^2+3) is 2xsin(x^2+3)+2x^3cos(x^2+3)