Question:
Differentiate w.r.t. \(x\) the function: \(sin^3x+cos^6x\)
Differentiate w.r.t. \(x\) the function: \(sin^3x+cos^6x\)
Updated On: Oct 19, 2023
Hide Solution
Verified By Collegedunia
Solution and Explanation
The correct answer is \(=3sinxcosx(sinx-2cos^4x)\)
Let \(y=sin^3x+cos^6x\)
\(∴\frac{dy}{dx}=\frac{d}{dx}(sin^3x)+\frac{d}{dx}(cos^6x)\)
\(=3sin^2x.\frac{d}{dx}(sinx)+6cos^5x.\frac{d}{dx}(cosx)\)
\(=3sin^2x.cosx+6cos^5x.(-sinx)\)
\(=3sinxcosx(sinx-2cos^4x)\)
Let \(y=sin^3x+cos^6x\)
\(∴\frac{dy}{dx}=\frac{d}{dx}(sin^3x)+\frac{d}{dx}(cos^6x)\)
\(=3sin^2x.\frac{d}{dx}(sinx)+6cos^5x.\frac{d}{dx}(cosx)\)
\(=3sin^2x.cosx+6cos^5x.(-sinx)\)
\(=3sinxcosx(sinx-2cos^4x)\)
Was this answer helpful?
0
0
Top Questions on Continuity and differentiability
- If $(x)^y = (y)^x$, then find $\frac{dy}{dx}$.
- CBSE CLASS XII - 2025
- Mathematics
- Continuity and differentiability
- Differentiate $y = \cos^{-1}\left( \frac{1 - x^2}{1 + x^2} \right)$ with respect to $x$, when $x \in (0, 1)$.
- CBSE CLASS XII - 2025
- Mathematics
- Continuity and differentiability
- Differentiate $y = \sin^{-1}(3x - 4x^3)$ with respect to $x$, for $x \in \left[ -\frac{1}{2}, \frac{1}{2} \right]$.
- CBSE CLASS XII - 2025
- Mathematics
- Continuity and differentiability
- (a) Differentiate $\sqrt{e^{\sqrt{2x}}}$ with respect to $e^{\sqrt{2x}}$ for $x>0$.
- CBSE CLASS XII - 2025
- Mathematics
- Continuity and differentiability
- If $y = a \cos(\log x) + b \sin(\log x)$, then $x^2y'' + xy'1$ is:
- CBSE CLASS XII - 2025
- Mathematics
- Continuity and differentiability
View More Questions
Questions Asked in CBSE CLASS XII exam
- A reaction is of second order with respect to a reactant. How is the rate of reaction affected if the concentration of the reactant is (i) doubled, (ii) reduced to half?
- CBSE CLASS XII - 2025
- Order of Reaction
Rupal, Shanu and Trisha were partners in a firm sharing profits and losses in the ratio of 4:3:1. Their Balance Sheet as at 31st March, 2024 was as follows:
(i) Trisha's share of profit was entirely taken by Shanu.
(ii) Fixed assets were found to be undervalued by Rs 2,40,000.
(iii) Stock was revalued at Rs 2,00,000.
(iv) Goodwill of the firm was valued at Rs 8,00,000 on Trisha's retirement.
(v) The total capital of the new firm was fixed at Rs 16,00,000 which was adjusted according to the new profit sharing ratio of the partners. For this necessary cash was paid off or brought in by the partners as the case may be.
Prepare Revaluation Account and Partners' Capital Accounts.- CBSE CLASS XII - 2025
- Partnership Accounts
- Explain giving three reasons why tropics show greatest levels of species diversity.
- CBSE CLASS XII - 2025
- Biodiversity
- The element of dilemma, between humanity and patriotism, elevates the character of Dr. Sadao in ‘The Enemy’. Support your answer with evidence from the text.
- CBSE CLASS XII - 2025
- Literature
- Find: \[ \frac{dy}{dx}, \quad \text{if} \quad y = x \tan x + \frac{\sqrt{x^2 + 1}}{2} \]
- CBSE CLASS XII - 2025
- Differentiation
View More Questions